Wyniki wyszukiwania - Biblioteka Nauki

1

Adaptacyjny algorytm sterowania manipulatora z elastycznością w złączach.

100%

Kozłowski K. , Sauer P.

Prace Naukowe Instytutu Cybernetyki Technicznej Politechniki Wrocławskiej. Konferencje

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1998

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tom Vol. 98, nr 44

129-140

PL

W artykule zaprezentowano algorytm sterowania adaptacyjnego dla manipulatora z elastycznością w złączach. Przedstawiony algorytm sterowania adaptacyjnego został wyprowadzony w oparciu o model zaproponowany przez Lorię i Ortegę w pracy [7] z uwzględnieniem istnienia tarcia oraz przekładni. Podstawowa zaleta prezentowanego algorytmu sterowania adaptacyjnego wypływa z prostoty pomiarów: model sterowania wymaga jedynie pomiaru położeń ogniw i wałów silników napędowych. Zaproponowany algorytm sterowania zaimplementowano w środowisku MATLAB (stacja SUN) i zweryfikowano na stanowisku eksperymentalnym. Stanowisko do weryfikacji składa się z : silnika prądu stałego, przekładni harmonicznej, systemu sterowania i obciążenia w postaci niewyważonej tarczy. W artykule zamieszczono przykładowe wykresy oraz wartości parametrów dla weryfikacji symulacyjnej i doświadczalnej.

EN

In this paper we present an adaptive control scheme for a manipulator with joint flexibility. This algorithm is a generalisation of the algorithm derived by Loria and Ortega [7] which includes friction modelling and uncertainty in the model parameters. Algorithm presented here assumes that only joint and motor positions are measured. A proof of the proposed algorithm is presented. Simulation and experimental results illustrate the theoretical consideration given in the paper.

2

Wybrane zagadnienia stabilności układów liniowych o zmiennych w czasie parametrach

100%

Polański A.

Zeszyty Naukowe. Automatyka / Politechnika Śląska

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2000

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tom z. 128

1-179

PL

W niniejszej pracy rozważa się problem stabilności układu liniowego o zmiennych w czasie parametrach. W modelu analizowanym w pracy zadane są mierzalnymi funkcjami czasu o wartościach w zadanych zbiorach wielościennych. Dla układów z przedstawionej klasy zagadnienie stabilności rozbija się na problemy częściowe (1) wykazania stabilności bądź niestabilności układu niezależne od zmian jego parametrów (absolutnej stabilności lub niestabilności) oraz (2) znalezienia takich przebiegów zmian parametrów w czasie, które stabilizują bądź destabilizują układ (strategii stabilizującej lub destabilizującej). Przedstawia się dwa sposoby podejścia do przedstawionych problemów. Pierwszy z nich obejmuje wyniki wywodzące się z teorii Floqueta. Podstawowym założeniem w tym podejściu jest okresowość zmian parametrów w czasie. Drugie podejście tworzą metody wykorzystujące twierdzenia teorii stabilności Lapunowa. Podstawowa idea polega na dobraniu funkcji Lapunowa, której pochodna wzdłuż trajektorii systemu jest, niezależnie od zmian wartości parametrów, funkcją określonego znaku.

EN

In this book the problem of stability of a linear system with time-varying parameters is considered. In the analyzed model the parameters are given by measurable time functions with values belonging to given polyhedral sets. For systems from the assumed class the stability problem is decomposed into subproblems (1) of proving stability or instability of the system for all possible parameter changes (absolute stability or instability) (2) of finding such time functions defining parameter changes which will ensure stabilization or destabilization of the system (stabilizing or destabilizing strategies). Two approaches to the introduced problems are presented. The first one includes results of Floquet theory. The main assumption in this approach is periodicity of parameter time changes. The second approach includes methods utilizing theorems fron Lyapunov stability theory. The main idea is in fitting a Lapunov function, which derivative along system trajectories is a definite function for all possible system parameter changes.

3

Non-quadratic performance design for Takagi-Sugeno fuzzy systems

75%

Bernal M. , Husek P.

International Journal of Applied Mathematics and Computer Science

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2005

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tom Vol. 15, no 3

383-391

EN

This paper improves controller synthesis of discrete Takagi-Sugeno fuzzy systems based on non-quadratic Lyapunov functions, making it possible to accomplish various kinds of control performance specifications such as decay rate conditions, requirements on control input and output and disturbance rejection. These extensions can be implemented via linear matrix inequalities, which are numerically solvable with commercially available software. The controller design is illustrated with an example.

4

The choice of the forms of Lyapunov functions for a positive 2D Roesser model

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Kaczorek T.

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tom Vol. 17, no 4

471-475

EN

The appropriate choice of the forms of Lyapunov functions for a positive 2D Roesser model is addressed. It is shown that for the positive 2D Roesser model: (i) a linear form of the state vector can be chosen as a Lyapunov function, (ii) there exists a strictly positive diagonal matrix P such that the matrix ATPA-P is negative definite. The theoretical deliberations will be illustrated by numerical examples.

5

Stability of an elastic column subjected to non-stationary compressive loads

75%

Ossowski A.

Engineering Transactions

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2005

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tom Vol. 53, iss. 3

335-343

EN

The problem of dynamic stability of an elastic column with pinned ends subjected to nonstationary compressive axial loads is considered. The method of optical Lyapunov functions for differential inclusions is applied to obtain sufficient conditions of stability of the column in the case of bounded loads. The obtained results, improving and generalising the classical solutions to the dynamic Euler problem, may be useful in designing civil engineering structures and mechanical systems consisting of compressed columns. The possibility of optimisation of the column characteristics with respect to its stability properties ( e. g. stability margins in the space of parameters) is pointed out.

6

Fundamental limitations of the decay of generalized energy in controlled (discrete-time) nonlinear systems subject to state and input constraints

75%

Selek I. , Ikonen E.

International Journal of Applied Mathematics and Computer Science

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2019

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tom Vol. 29, no. 4

629--639

EN

This paper is devoted to the analysis of fundamental limitations regarding closed-loop control performance of discrete-time nonlinear systems subject to hard constraints (which are nonlinear in state and manipulated input variables). The control performance for the problem of interest is quantified by the decline (decay) of the generalized energy of the controlled system. The paper develops (upper and lower) barriers bounding the decay of the system’s generalized energy, which can be achieved over a set of asymptotically stabilizing feedback laws. The corresponding problem is treated without the loss of generality, resulting in a theoretical framework that provides a solid basis for practical implementations. To enhance understanding, the main results are illustrated in a simple example.

7

Badanie stabilności układu hybrydowego z zastosowaniem wielokrotnej przedziałami liniowej funkcji Lapunowa

63%

Starosolski Z.

Zeszyty Naukowe. Automatyka / Politechnika Śląska

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2006

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tom z. 146

85-104

PL

W niniejszej pracy badano stabilność układu hybrydowego z zastosowaniem wielokrotnej funkcji Lapunowa. Do parametryzacji wielokrotnej funkcji Lapunowa użyto funkcji przedziałami liniowej. Rozważano układ hybrydowy złożony z dwóch dynamik przełączanych w zależności od stanu dyskretnego i liniowej funkcji przełączającej. Cechą charakterystyczną badanego układu jest poruszanie się po trajektoriach dwóch różnych dynamik w tym samym regionie płaszczyzny stanu. Stabilność danego układu jest analizowana przez rozwiązanie problemu programowania liniowego (PPL). W wyniku rozwiązania PPL otrzymuje się wartości przedziałami liniowej wielokrotnej funkcji Lapunowa (PLWFL). W pracy zostały przedstawione warunki konieczne, jakie musi spełniać PLWFL, aby badany układ hybrydowy był asymptotycznie stabilny.

EN

In the paper a study of application of piecewise linear Lyapunov function as a Multiple Lyapunov function for analyzing the stability of hybrid system is presented. An example of hybrid system composed of two linear dynamics with switching is analyzed. The switching is controlled by a discrete control function. Both dynamics are asymptocally stable and both are defined under common region of the state space. The stability of hybrid system is proved by solving the linear programming problem. The conditions for asymptotic stability of hybrid linear system based on Piecewise Linear Multiple Lyapunov Function are presented.

8

T–S fuzzy BIBO stabilisation of non-linear systems under persistent perturbations using fuzzy Lyapunov functions and non-PDC control laws

63%

Salcedo J. V. , Martínez M. , García-Nieto S. , Hilario A.

International Journal of Applied Mathematics and Computer Science

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2020

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tom Vol. 30, no. 3

529--550

EN

This paper develops an innovative approach for designing non-parallel distributed fuzzy controllers for continuous-time non-linear systems under persistent perturbations. Non-linear systems are represented using Takagi–Sugeno fuzzy models. These non-PDC controllers guarantee bounded input bounded output stabilisation in closed-loop throughout the computation of generalised inescapable ellipsoids. These controllers are computed with linear matrix inequalities using fuzzy Lyapunov functions and integral delayed Lyapunov functions. LMI conditions developed in this paper provide non-PDC controllers with a minimum ⋆-norm (upper bound of the 1-norm) for the T–S fuzzy system under persistent perturbations. The results presented in this paper can be classified into two categories: local methods based on fuzzy Lyapunov functions with guaranteed bounds on the first derivatives of membership functions and global methods based on integral-delayed Lyapunov functions which are independent of the first derivatives of membership functions. The benefits of the proposed results are shown through some illustrative examples.

9

Adaptive backstepping tracking control for an over-actuated DP marine vessel with inertia uncertainties

63%

Witkowska A. , Śmierzchalski R.

International Journal of Applied Mathematics and Computer Science

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2018

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tom Vol. 28, no. 4

679--693

EN

Designing a tracking control system for an over-actuated dynamic positioning marine vessel in the case of insufficient information on environmental disturbances, hydrodynamic damping, Coriolis forces and vessel inertia characteristics is considered. The designed adaptive MIMO backstepping control law with control allocation is based on Lyapunov control theory for cascaded systems to guarantee stabilization of the marine vessel position and heading. Forces and torque computed from the adaptive control law are allocated to individual thrusters by employing the quadratic programming method in combination with the cascaded generalized inverse algorithm, the weighted least squares algorithm and the minimal least squares algorithm. The effectiveness of the proposed control scheme is demonstrated by simulations involving a redundant set of actuators. The evaluation criteria include energy consumption, robustness, as well accuracy of tracking during typical vessel operation.

10

Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays

63%

Raja R. , Sakthivel R. , Anthoni S. M. , Kim H.

International Journal of Applied Mathematics and Computer Science

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2011

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tom Vol. 21, no 1

127-135

EN

The paper is concerned with stability analysis for a class of impulsive Hopfield neural networks with Markovian jumping parameters and time-varying delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process. By employing a Lyapunov functional approach, new delay-dependent stochastic stability criteria are obtained in terms of linear matrix inequalities (LMIs). The proposed criteria can be easily checked by using some standard numerical packages such as theMatlab LMI Toolbox. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some results existing in the literature.

11

Convergence method, properties and computational complexity for Lyapunov games

63%

Clempner J. B. , Poznyak A. S.

International Journal of Applied Mathematics and Computer Science

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2011

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tom Vol. 21, no 2

349-361

EN

We introduce the concept of a Lyapunov game as a subclass of strictly dominated games and potential games. The advantage of this approach is that every ergodic system (repeated game) can be represented by a Lyapunov-like function. A direct acyclic graph is associated with a game. The graph structure represents the dependencies existing between the strategy profiles. By definition, a Lyapunov-like function monotonically decreases and converges to a single Lyapunov equilibrium point identified by the sink of the game graph. It is important to note that in previous works this convergence has not been guaranteed even if the Nash equilibrium point exists. The best reply dynamics result in a natural implementation of the behavior of a Lyapunov-like function. Therefore, a Lyapunov game has also the benefit that it is common knowledge of the players that only best replies are chosen. By the natural evolution of a Lyapunov-like function, no matter what, a strategy played once is not played again. As a construction example, we show that, for repeated games with bounded nonnegative cost functions within the class of differentiable vector functions whose derivatives satisfy the Lipschitz condition, a complex vector-function can be built, where each component is a function of the corresponding cost value and satisfies the condition of the Lyapunov-like function. The resulting vector Lyapunov-like function is a monotonic function which can only decrease over time. Then, a repeated game can be represented by a one-shot game. The functionality of the suggested method is successfully demonstrated by a simulated experiment.

12

Speed Sensorless Control of Induction Motor Based on a Non-Linear Flux and Speed Observer with Parameters Estimation and Considering Iron Loss

63%

Alemi-Rostami M. , Abrishamifar A.

Przegląd Elektrotechniczny

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2013

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tom R. 89, nr 3a

89--97

EN

In this paper, a control method is presented for induction motor which offers high efficiency and high dynamics even considering the influences of iron loss. Recently, research to consider the influences of iron loss has been made in the vector control of an induction motor. Vector control method is a quite complex task which demands precise information about the rotor speed and the position of the magnetic flux. The vector control method presented in this paper, estimates both rotor speed and amplitude magnetic flux rotor. However, there are also applications in which even speed sensors should be omitted. In this method, three-phase motor currents and DC link voltage are measured by means of a nonlinear observer and considering the Lyapunov function for current error, motor parameters, rotor shaft and position of flux are estimated. To stabilize the control system, the Lyapunov function for error, is used. Then, using the genetic algorithm, the value of controlling coefficients their and general effects on system's behavior are obtained. The simulation and experimental results confirm the resistant performance and the proper dynamic efficiency of this method.

PL

W artykule przedstawiono algorytm sterowania maszyną indukcyjną, uwzględniający straty w żelazie. Sterowanie opiera się na bezczujnikowym pomiarze prędkości obrotowej, przy pomocy obserwatora. Korzystając z pomiarów prądów fazowych i napięcia DC-link, z funkcji Lyapunov’a wyznaczana jest prędkość i strumień wirnika. Implementacja algorytmu genetycznego pozwoliła na ocenę wpływu współczynników regulacji na odpowiedź układu. Przedstawiono wyniki symulacyjne i eksperymentalne.

13

One DOF robot manipulator control through type-2 fuzzy robust adaptive controller

63%

Naderolasli A. , Chatraei A.

Journal of Automation Mobile Robotics and Intelligent Systems

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2019

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tom Vol. 13, No. 1

65--70

EN

In this article, the one DOF robot manipulator control is assessed through second type robust fuzzy-adaptive controller. The objective is to obtain a tracking path with appropriate accuracy. The stability of the closed loop system is verified through Lyapunov stability theory and the efficiency of tracking is analyzed subject to the constraints and uncertainty. In order to design the fuzzy controller a set of if-then fuzzy rules are considered which describe the system input-output behavior. Simulation and the results of the experiments on the one DOF robots indicate the effectiveness of the proposed methods.

14

A new robust approach to MCS algorithms. Application to an AC machine

63%

Naceri F. , Belkacem S.

Archives of Electrical Engineering

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2006

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tom Vol. 55, nr 2

163-178

EN

The robustness of MCS algorithms against rapidly varying system parameters, external disturbances and system non-linearity is investigated. The MCS algorithm is a signifiant developpment of MRAC and is similary based on the hyperstability theory of Popov. The hyperstability theory guarantees the global asymptotic stability of the error vector (i.e. the difference between the reference model and system states). Finally a new approach has been successfully implemented to Field-Oriented Controlled drive. Discussion on theoretical aspects, such as, selection of a reference model, stability analysis, gain adaptive and steady state error are included. Results of simulations are also presented.

PL

Przeanalizowano odporność algorytmów syntezy minimalnego sterownika przy szybkozmiennych wartościach parametrów układu, zakłóceniach zewnętrznych i przy nieliniowości. Algorytm syntezy minimalnego sterownika jest istotnym krokiem w rozwoju sterowania adaptacyjnego z modelem odniesienia, opartym na teorii hyperstabilności Popowa. Zapewnia ona szeroką stabilność asymetryczną wektora błędu (różnicy między stanami modelu odniesienia i układu). Nowe podejście zastosowano pomyślnie w sterowaniu polowo-zorientowanym. Przedyskutowano takie zagadnienia teoretyczne jak wybór modelu odniesienia, analizę stabilności, błąd doboru wzmocnienia i błąd w stanie ustalonym. Przedstawiono rezultaty badań symulacyjnych.

15

On three methods for bounding the rate of convergence for some continuous-time Markov chains

63%

Zeifman A. , Satin Y. , Kryukova A. , Razumchik R. , Kiseleva K. , Shilova G.

International Journal of Applied Mathematics and Computer Science

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2020

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tom Vol. 30, no. 2

251--266

EN

Consideration is given to three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is particularly well suited to describe evolutions of the total number of customers in (in)homogeneous M/M/S queueing systems with possibly state-dependent arrival and service intensities, batch arrivals and services. One of the methods is based on the logarithmic norm of a linear operator function; the other two rely on Lyapunov functions and differential inequalities, respectively. Less restrictive conditions (compared with those known from the literature) under which the methods are applicable are being formulated. Two numerical examples are given. It is also shown that, for homogeneous birth-death Markov processes defined on a finite state space with all transition rates being positive, all methods yield the same sharp upper bound.

16

Iterated function systems generated by strict contractions and place-dependent probabilities

63%

Zaharopol R.

Bulletin of the Polish Academy of Sciences. Mathematics

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2000

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tom Vol. 48, no 4

429--438

EN

Let (w[sub l], w[sub 2],...,w[sub k];p[sub 1],p[sub 2],...p[sub k]) be an iterated function system (IFS for short) with continuous place-dependent probabilities, defined on a metric space (X, d). Assume that every closed ball in X is compact. Our main result is that the IFS has an attractive probability measure whenever the following three conditions are satisfied: (1) w[sub i] : X --> X is a strict contraction for every i = 1,...,k. (2) sum[...]p[sub i](x)p[sub i](y) > 0 for every x, y [belongs to] X. (3) There exists p > 0 in R such that [...] for every x, y [belongs to] X and j = l, 2,...,k. Note that we do not require the p[sub i]'s to be even uniformly continuous. This research was motivated by a question of Barnsley, Demko, Elton, and Geronimo, [1, p. 373], concerning IFS which satisfy only condition (1). We construct a family C of IFS which we use to answer the question. Our main result allows us to distinguish IFS in C which possess attractive probabilities.

17

A new fuzzy Lyapunov approach to non-quadratic stabilization of Takagi-Sugeno fuzzy models

63%

Abdelmalek I. , Goléa N. , Hadjili M. L.

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tom Vol. 17, no 1

39-51

EN

In this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization. The proposed approach is based on two assumptions. The first one relates to a proportional relation between multiple Lyapunov functions and the second one considers an upper bound to the time derivative of the premise membership functions. To illustrate the advantages of our proposal, four examples are given.

18

A backstepping approach to ship course control

63%

Witkowska A. , Tomera M. , Śmierzchalski R.

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tom Vol. 17, no 1

73-85

EN

As an object of course control, the ship is characterised by a nonlinear function describing static manoeuvring characteristics that reflect the steady-state relation between the rudder deflection and the rate of turn of the hull. One of the methods which can be used for designing a nonlinear ship course controller is the backstepping method. It is used here for designing two configurations of nonlinear controllers, which are then applied to ship course control. The parameters of the obtained nonlinear control structures are tuned to optimise the operation of the control system. The optimisation is performed using genetic algorithms. The quality of operation of the designed control algorithms is checked in simulation tests performed on the mathematical model of a tanker. In order to obtain reference results to be used for comparison with those recorded for nonlinear controllers designed using the backstepping method, a control system with the PD controller is examined as well.

19

Extended Lie algebraic stability analysis for switched systems with continuous-time and discrete–time subsystems

63%

Zhai G. , Xu X. , Lin H. , Liu D.

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tom Vol. 17, no 4

447-454

EN

We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.

20

Criteria for Stability of Uncertain Linear Systems With Time-Varying Delay

63%

Han Q. L. , Gu K.

International Journal of Applied Mathematics and Computer Science

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2000

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tom Vol. 10, no 2

205-225

EN

This paper focuses on the stability problem for uncertain linear systems with time-varying delays. Based on a discretized Lyapunov functional approach, delay-dependent criteria that are formulated in terms of linear matrix inequalities are proposed to guarantee asymptotic stability for such systems. Numerical examples are also included to show the effectiveness of the method.