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  1. 35 International Journal of Applied Mathematics and Computer Science
  2. 12 Przegląd Elektrotechniczny
  3. 5 Vibrations in Physical Systems
  4. 4 Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
  5. 3 Bulletin of the Polish Academy of Sciences. Technical Sciences
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  1. 4 Kaczorek T.
  2. 4 Kaczorek Tadeusz
  3. 4 Świszcz P.
  4. 3 Bańka S.
  5. 3 Dworak P.
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  1. 1 2026
  2. 7 2025
  3. 2 2024
  4. 1 2023
  5. 3 2022
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1
Content available On the Global stability of fractional feedback nonlinear systems with interval matrices of positive linear parts and application to electrical circuits
Kaczorek Tadeusz
International Journal of Applied Mathematics and Computer Science
|
2026
|
Vol. 36, no. 1
5--11
EN
The global stability of fractional multi-inputs multi-outputs continuous-time nonlinear feedback systems with interval matrices of positive linear parts and application to electrical circuits is investigated. New sufficient conditions for the global stability of fractional nonlinear systems are given. The new stability conditions are applied to nonlinear electrical circuits and demonstrated on a simple example of a fractional nonlinear feedback system with a positive linear part.
2
Content available Testing the SDC memristors in three phase systems
Garda Bartłomiej, Bednarz Karol
Przegląd Elektrotechniczny
|
2025
|
R. 101, nr 2
52--55
EN
The objective outlined in the paper is to conduct reliable measurement tests on memristor behavior in three-phase systems. Memristors, acting as nonlinear elements, exhibit intriguing phenomena within such systems. Various configurations, including Delta and Wye connections with three and four wires, have been tested. The collected data has been analyzed and presented, with additional frequency analysis using FFT and assessment of total harmonic distortion factors. The acquired data has been modelled using the MMS memristor model and compared with the actual data.
PL
W artykule przedstawiono wyniki testów pomiarowych opisujących zachowania memrystorów w systemach trójfazowych. Memrystory, jako nieliniowe elementy, wykazują˛ intrygujące zjawiska w takich systemach. Przetestowano różne konfiguracje, w tym połączenia w trójkąt, w gwiazdę z trzema i czterema przewodami. Zebrane dane zostały przeanalizowane i przedstawione. Dokonano analizy częstotliwościowej FFT oraz wyznaczono współczynniki całkowitego zniekształcenia harmonicznego THD. Następnie uzyskane wyniki pomiarowe zostały zamodelowane z wykorzystaniem modelu memrystora MMS i porównane z danymi rzeczywistymi.
3
Content available Influence of beam material on the voltage and power responses in a nonlinear electromagnetic energy harvester
Gabor Rafał, Kulik Marcin
Przegląd Elektrotechniczny
|
2025
|
R. 101, nr 11
33--40
EN
This study investigates how the choice of beam material affects the dynamic performance of a nonlinear electromagnetic energy harvester. Four materials- carbon fiber, fiberglass, aluminum, and ABS - were analyzed by optimizing their beam cross-sections (at a fixed length) to achieve a common resonance frequency of 35 Hz. Despite identical natural frequencies, modal and dynamic simulations revealed notable differences in vibration response, voltage output, power generation, and stress distribution. Composite materials, particularly carbon fiber and fiberglass, produced higher output voltages and power, while aluminum offered a wider operational bandwidth. Stress analyses under identical displacements showed significant variation in maximum stress, driven primarily by differences in Young’s modulus. The presented methodology supports materialand geometry-aware design of efficient, durable energy harvesters for use in autonomous, vibration-powered devices.
PL
Niniejszy artykuł ukazuje, w jaki sposób wybór materiału belki wpływa na charakterystyki dynamiczne nieliniowego elektromagnetycznego układu pozyskiwania energii. Cztery materiały - włókno węglowe, włókno szklane, aluminium oraz ABS - zostały przeanalizowane poprzez optymalizację przekrojów poprzecznych belek (przy stałej długości) w celu uzyskania wspólnej częstotliwości rezonansowej wynoszącej 35 Hz. Pomimo identycznych częstotliwości własnych, symulacje modalne i dynamiczne ujawniły istotne różnice w odpowiedzi drganiowej, generowanym napięciu, wytwarzanej mocy oraz rozkładzie naprężeń. Materiały kompozytowe, w szczególności włókno węglowe i szklane, wykazały wyższe wartości napięcia wyjściowego i mocy, natomiast aluminium charakteryzowało się szerszym pasmem roboczym. Analizy naprężeń przy identycznych przemieszczeniach wykazały znaczną zmienność maksymalnych naprężeń, wynikającą głównie z różnic w module Younga. Zaprezentowana metodologia wspiera projektowanie wydajnych i trwałych układów pozyskiwania energii, uwzględniających materiał i geometrię, przeznaczonych do zastosowań w autonomicznych urządzeniach zasilanych drganiami.
4
Content available A computationally tractable stabilizing predictive controller with fuzzy cost functions for discrete-time nonlinear systems
Teniou Samir
Przegląd Elektrotechniczny
|
2025
|
R. 101, nr 11
309--317
EN
A novel stabilizing controller for discrete-time nonlinear systems that uses a fuzzy receding horizon feedback control law is presented. The control input and the state variables are both subject to constraints in this controller. The membership functions of the fuzzy goals and the fuzzy constraints in the fuzzy cost function handles those imposed constraints. We prove asymptotic stability of the infinite horizon fuzzy optimal control law that uses the product as an aggregation operator with respect to time. This result is essential for showing that the finite horizon’s closed-loop asymptotic stability can be guaranteed using just the standard final region constraint and, in this case, the switching to the local stabilizing controller will not be necessary inside this final region. The main contribution of the paper is a practical and computationally tractable suboptimal fuzzy receding horizon control scheme that is asymptotically stabilizing. The effectiveness of the proposed scheme is shown by simulations on a continuous stirred tank reactor (CSTR) model.
PL
Przedstawiono nowatorski regulator stabilizujący dla dyskretnych układów nieliniowych, który wykorzystuje prawo sterowania ze sprzężeniem zwrotnym z rozmytym horyzontem ustępującym. Zarówno sygnał wejściowy sterowania, jak i zmienne stanu podlegają ograniczeniom w tym regulatorze. Funkcje przynależności celów rozmytych i ograniczenia rozmyte w funkcji kosztu rozmytego uwzględniają te narzucone ograniczenia. Dowodzimy asymptotycznej stabilności prawa sterowania optymalnego rozmytego o nieskończonym horyzoncie, które wykorzystuje iloczyn jako operator agregacji względem czasu. Wynik ten jest kluczowy dla wykazania, że asymptotyczna stabilność zamkniętej pętli skończonego horyzontu może być zagwarantowana przy użyciu jedynie standardowego ograniczenia obszaru końcowego, a w tym przypadku przełączanie na lokalny regulator stabilizujący nie będzie konieczne wewnątrz tego obszaru końcowego. Głównym wkładem artykułu jest praktyczny i łatwy w obliczeniach suboptymalny schemat sterowania z rozmytym horyzontem ustępującym, który jest asymptotycznie stabilizujący. Skuteczność proponowanego schematu została wykazana za pomocą symulacji przeprowadzonych na modelu reaktora zbiornikowego z ciągłym mieszaniem.
5
Content available remote Controllability of Impulsive Second-order System using Functional Analytic Approach
Badiyani Sanket, Chudasama Neeta, Vaghela Vimalkumar, Patel Khushi, Shah Vishant
Mathematica Applicanda
|
2025
|
Vol 53, no. 2
167--183
EN
This article examines the exact controllability of second-order nonlinear abstract impulsive systems. The controllability of linear impulsive systems is addressed through the application of operator theory, while the analysis of nonlinear systems leverages nonlinear functional analysis and the fixed point theorem. An illustrative example is provided to reinforce the theoretical findings, demonstrating the practical validity of the results.
PL
W niniejszym artykule analizowana jest dokładna sterowalność nieliniowych abstrakcyjnych układów impulsowych drugiego rzędu. Sterowalność liniowych układów impulsowych jest analizowana poprzez zastosowanie teorii operatorów, natomiast analiza układów nieliniowych wykorzystuje nieliniową analizę funkcjonalną i twierdzenie o punkcie stałym. W celu wzmocnienia ustaleń teoretycznych przedstawiono przykład ilustrujący praktyczną ważność wyników.
6
Content available Robustness enhancement of a dynamic object model against adversarial attacks
Sopot Wojciech, Wachel Paweł, Mzyk Grzegorz
International Journal of Applied Mathematics and Computer Science
|
2025
|
Vol. 35, no. 4
591--600
EN
The aim of this work is to find a compromise between the accuracy of reproducing the behaviour of a nominal (Wiener-type) object examined in a laboratory under noise-free conditions and its robustness to intentional external attacks disrupting the input signal. By linearizing the model at the operating points and replacing the computationally expensive minimax optimization criterion with a simpler one, we construct a technique that leads to models robust to adversarial attacks of bounded intensity. Simulation experiments demonstrate the robustness of the obtained models against adversarial disruptions, highlighting the method’s potential applications in fields requiring high resilience, such as control systems and safety-critical environments.
7
Content available A unified convex combination approach to switched uncertain nonlinear systems
Chang Yufang, Zhai Guisheng, Fu Bo
International Journal of Applied Mathematics and Computer Science
|
2025
|
Vol. 35, no. 1
117--128
EN
We address a unified convex combination approach to a class of switched uncertain nonlinear systems, focusing on quadratic stability and L2 gain. In each subsystem, there are norm-bounded uncertainties in the system matrix and nonlinear terms with quadratic constraints. The proposed convex combination is original and unified in the sense of incorporating not only the nominal subsystem matrices but also uncertainty and quadratic constraints in the same form. When there is no single subsystem having the desired performance but a convex combination of subsystems does, we design a switching law so that the switched system achieves the same performance. Moreover, the discussion is extended to switching state feedback and its application to a boost converter.
8
Content available Design of fuzzy dynamic decoupler for a class of two-inputs two-outputs nonlinear systems
Król Szymon, Dworak Paweł
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2025
|
Vol. 73, nr 1
art. no. e152218
EN
This paper deals with the problem of designing a dynamic decoupler for a class of two-inputs two-outputs nonlinear MIMO systems with experimentally modeled dynamics. The work describes the well-known linear theory of dynamic decoupling of TITO plants and discusses problems related to its application to nonlinear systems. The solution of constructing a fuzzy dynamic decoupler with two possible approaches is proposed. The paper gives a practical example of the synthesis of such a system for the air heater, which is an example of nonlinear thermal plant.
9
Content available Analytical modeling of the harmonic distortion caused by squeeze film damping in MEMS-based acoustic transducers
Melnikov Anton, Schenk Hermann A.G., Wall Franziska
Vibrations in Physical Systems
|
2024
|
Vol. 35, nr 1
art. no. 2024106
EN
Miniaturized microelectromechanical system (MEMS) microspeakers are currently trending in the development of acoustic transducers. When a transducer is scaled down to fit on a microelectronic chip, its physics differ from the macroscopic world, and some common modeling assumptions become invalid. One of the effects observed in MEMS microspeakers is nonlinear squeeze film damping. Understanding this effect is crucial, as non-linearities in the speaker can result in perceptible harmonic distortions, which are undesirable in audio applications. In this study, we analyze the influence of squeeze film damping on harmonic distortions using a lumped parameter model of a MEMS microspeaker. This leads to a nonlinear ordinary differential equation, and an approximate analytical solution for moderate non-linearities is obtained using homotopy. We present our solution strategy, including the resulting closed-form expression, and verify our findings against numerical solutions.
10
Content available Dynamic sliding mode control based on a full-order observer: Underactuated electro-mechanical system regulation
Ordaz Patricio, Romero-Trejo Hugo, Cuvas Carlos, Sandre Omar
International Journal of Applied Mathematics and Computer Science
|
2024
|
Vol. 34, no. 1
29--43
EN
This paper concerns the synthesis of a nonlinear robust output controller based on a full-order observer for a class of uncertain disturbed systems. The proposed method guarantees that, in finite time, the system trajectories go inside a minimal neighborhood ultimately bounded. To this end, the attractive ellipsoid method is enhanced by applying the dynamic sliding mode control performance properties. Furthermore, in order to guarantee the stability of the trajectory around the trivial solution in the uniform-ultimately bounded sense, the feasibility of a specific matrix inequality problem is provided. With this feasible set of matrix inequalities, the separation principle of the controller/observer scheme considered also holds. To achieve a system performance improvement, a numerical algorithm based on the small size ultimate bound is presented. Finally, to illustrate the theoretical performance of the designed controller/observer, a numerical example dealing with the stabilization of a disturbed electromechanical system with uncertain and unmodeled dynamics is presented.
11
Content available Robust flat filtering control of a two degrees of freedom helicopter subject to tail rotor disturbances
Sánchez-Meza Victor-Gabriel, Lozano-Hernández Yair, Gutiérrez-Frías Octavio, Lozada-Castillo Norma, Luviano-Juárez Alberto
International Journal of Applied Mathematics and Computer Science
|
2023
|
Vol. 33, no. 4
521--535
EN
This article deals with modelling and a flatness-based robust trajectory tracking scheme for a two degrees of freedom helicopter, which is subject to four types of tail rotor disturbances to validate the control scheme robustness. A mathematical model of the system, its differential flatness and a differential parametrization are obtained. The flat filtering control is designed for the system control with a partially known model, assuming the non-modelled dynamics and the external disturbances (specially the tail rotor ones) to be rejected by means of an extended state model (ultra-local model). Numerical and experimental assessments are carried out on a characterized prototype whose yaw angle (ψ), given by the z axis, is in free form, while the pitch angle (θ), which results from rotation about the y axis, is mechanically restricted. The proposed controller performance is tested through a set of experiments in trajectory tracking tasks with different disturbances in the tail rotor, showing robust behaviour for the different disturbances. Besides, a comparison study against a widely used controller of LQR type is carried out, in which the proposed controller achieves better results, as illustrated by a performance index.
12
Content available Global stability of discrete-time feedback nonlinear systems with descriptor positive linear parts and interval state matrices
Kaczorek Tadeusz, Ruszewski Andrzej
International Journal of Applied Mathematics and Computer Science
|
2022
|
Vol. 32, no. 1
5--10
EN
The global stability of discrete-time nonlinear systems with descriptor positive linear parts, positive scalar feedbacks and interval state matrices is addressed. Sufficient conditions for the global stability of this class of nonlinear systems are established. The effectiveness of these conditions is illustrated using numerical examples.
13
Content available Fault-tolerant tracking control for a non-linear twin-rotor system under ellipsoidal bounding
Kukurowski Norbert, Mrugalski Marcin, Pazera Marcin, Witczak Marcin
International Journal of Applied Mathematics and Computer Science
|
2022
|
Vol. 32, no. 2
171--183
EN
A novel fault-tolerant tracking control scheme based on an adaptive robust observer for non-linear systems is proposed. Additionally, it is presumed that the non-linear system may be faulty, i.e., affected by actuator and sensor faults along with the disturbances, simultaneously. Accordingly, the stability of the robust observer as well as the fault-tolerant tracking controller is achieved by using the ℋ∞ approach. Furthermore, unknown actuator and sensor faults and states are bounded by the uncertainty intervals for estimation quality assessment as well as reliable fault diagnosis. This means that narrow intervals accompany better estimation quality. Thus, to cope with the above difficulty, it is assumed that the disturbances are over-bounded by an ellipsoid. Consequently, the performance and correctness of the proposed fault-tolerant tracking control scheme are verified by using a non-linear twin-rotor aerodynamical laboratory system.
14
Content available A data driven fault isolation method based on reference faulty situations with application to a nonlinear chemical process
Ragot José, Mourot Gilles, Kallas Maya
International Journal of Applied Mathematics and Computer Science
|
2022
|
Vol. 32, no. 4
635--655
EN
The diagnosis of systems is one of the major steps in their control and its purpose is to determine the possible presence of dysfunctions, which affect the sensors and actuators associated with a system but also the internal components of the system itself. On the one hand, the diagnosis must therefore focus on the detection of a dysfunction and, on the other hand, on the physical localization of the dysfunction by specifying the component in a faulty situation, and then on its temporal localization. In this contribution, the emphasis is on the use of software redundancy applied to the detection of anomalies within the measurements collected in the system. The systems considered here are characterized by non-linear behaviours whose model is not known a priori. The proposed strategy therefore focuses on processing the data acquired on the system for which it is assumed that a healthy operating regime is known. Diagnostic procedures usually use this data corresponding to good operating regimes by comparing them with new situations that may contain faults. Our approach is fundamentally different in that the good functioning data allow us, by means of a non-linear prediction technique, to generate a lot of data that reflect all the faults under different excitation situations of the system. The database thus created characterizes the dysfunctions and then serves as a reference to be compared with real situations. This comparison, which then makes it possible to recognize the faulty situation, is based on a technique for evaluating the main angle between subspaces of system dysfunction situations. An important point of the discussion concerns the robustness and sensitivity of fault indicators. In particular, it is shown how, by non-linear combinations, it is possible to increase the size of these indicators in such a way as to facilitate the location of faults.
15
Content available New multipoint algorithm for eliminating chaotic vibrations in complex non-linear systems
Basiński Radosław, Siwek Krzysztof
Przegląd Elektrotechniczny
|
2021
|
R. 97, nr 6
91--96
EN
The paper presents a very effective algorithm for stabilizing unstable periodic orbits, consisting of slight changes in selected parameters of a chaotic system at any time of sampling. Modification of the parameters leads to minimization of the distance of the phase trajectory from the fixed point on the cross-section of the generalized Poincaré map. By modifying several parameters, it is possible to effectively eliminate chaotic vibrations in complex non-linear dynamical systems in the presence of strong disturbances and noise.
PL
W pracy przedstawiono efektywny algorytm stabilizacji niestabilnych orbit okresowych, polegający na niewielkich zmianach wybranych parametrów układu chaotycznego w każdej chwili próbkowania. Modyfikacja parametrów prowadzi do minimalizacji odległość trajektorii fazowej od punktu stałego na przekroju uogólnionego odwzorowania Poincarégo. Realizacja zagadnienia sterowania poprzez zmianę kilku parametrów umożliwia efektywną eliminację drgań chaotycznych w złożonych nieliniowych układach dynamicznych w obecności silnych zakłóceń i szumów.
16
Content available Conditions and a computation method of the constrained regulation problem for a class of fractional-order nonlinear continuous-time systems
Si Xindong, Yang Hongli, Ivanov Ivan G.
International Journal of Applied Mathematics and Computer Science
|
2021
|
Vol. 31, no. 1
17--28
EN
The constrained regulation problem (CRP) for fractional-order nonlinear continuous-time systems is investigated. New existence conditions of a linear feedback control law for a class of fractional-order nonlinear continuous-time systems under constraints are proposed. A computation method for solving the CRP for fractional-order nonlinear systems is also presented. Using the comparison principle and positively invariant set theory, conditions guaranteeing positive invariance of a polyhedron for fractional-order nonlinear systems are established. A linear feedback controller model and the corresponding algorithm of the CRP for fractional nonlinear systems are also proposed by using the obtained conditions. The presented model of the CRP is formulated as a linear programming problem, which can be easily implemented from a computational point of view. Numerical examples illustrate the proposed method.
17
Content available A computationally inexpensive algorithm for determining outer and inner enclosures of nonlinear mappings of ellipsoidal domains
Rauh Andreas, Jaulin Luc
International Journal of Applied Mathematics and Computer Science
|
2021
|
Vol. 31, no. 3
399--415
EN
A wide variety of approaches for set-valued simulation, parameter identification, state estimation as well as reachability, observability and stability analysis for nonlinear discrete-time systems involve the propagation of ellipsoids via nonlinear functions. It is well known that the corresponding image sets usually possess a complex shape and may even be nonconvex despite the convexity of the input data. For that reason, domain splitting procedures are often employed which help to reduce the phenomenon of overestimation that can be traced back to the well-known dependency and wrapping effects of interval analysis. In this paper, we propose a simple, yet efficient scheme for simultaneously determining outer and inner ellipsoidal range enclosures of the solution for the evaluation of multi-dimensional functions if the input domains are themselves described by ellipsoids. The Hausdorff distance between the computed enclosure and the exact solution set reduces at least linearly when decreasing the size of the input domains. In addition to algebraic function evaluations, the proposed technique is-for the first time, to our knowledge-employed for quantifying worst-case errors when extended Kalman filter-like, linearization-based techniques are used for forecasting confidence ellipsoids in a stochastic setting.
18
Content available Global stability of nonlinear feedback systems with fractional positive linear parts
Kaczorek Tadeusz
International Journal of Applied Mathematics and Computer Science
|
2020
|
Vol. 30, no. 3
493--499
EN
The global (absolute) stability of nonlinear systems with fractional positive and not necessarily asymptotically stable linear parts and feedbacks is addressed. The characteristics u = f(e) of the nonlinear parts satisfy the condition k1e ≤ f(e) ≤ k2e for some positive k1 and k2. It is shown that the fractional nonlinear systems are globally asymptotically stable if the Nyquist plots of the fractional positive linear parts are located on the right-hand side of the circles (−1/k1,−1/k2).
19
Content available Two-stage instrumental variables identification of polynomial Wiener systems with invertible nonlinearities
Janczak Andrzej, Korbicz Józef
International Journal of Applied Mathematics and Computer Science
|
2019
|
Vol. 29, no. 3
571--580
EN
A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter estimates are consistent, the number of parameters of the transformed Wiener model is much greater than that of the original one. Moreover, there is no unique relationship between parameters of the inverse nonlinear function and those of the transformed Wiener model. In Stage II, based on the assumption that the linear dynamic model is already known, parameters of the inverse nonlinear function are estimated uniquely using the IV method. In this way, not only is the parameter redundancy removed but also the parameter estimation accuracy is increased. A numerical example is included to demonstrate the practical effectiveness of the proposed approach.
20
Content available LMI-based robust control of uncertain nonlinear systems via polytopes of polynomials
Sánchez Marcelino, Bernal Miguel
International Journal of Applied Mathematics and Computer Science
|
2019
|
Vol. 29, no. 2
275--283
EN
This investigation is concerned with robust analysis and control of uncertain nonlinear systems with parametric uncertainties. In contrast to the methodologies from the field of linear parameter varying systems, which employ convex structures of the state space representation in order to perform analysis and design, the proposed approach makes use of a polytopic form of a generalisation of the characteristic polynomial, which proves to outperform former results on the subject. Moreover, the derived conditions have the advantage of being cast as linear matrix inequalities under mild assumptions.
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