PL
 |
EN
Ograniczanie wyników
Czasopisma help
  1. 21 International Journal of Applied Mathematics and Computer Science
  2. 7 Przegląd Elektrotechniczny
  3. 6 Zeszyty Naukowe. Automatyka / Politechnika Śląska
  4. 3 Bulletin of the Polish Academy of Sciences. Technical Sciences
  5. 3 PAK
Więcej...
Autorzy help
  1. 17 Kaczorek T.
  2. 6 Kaczorek Tadeusz
  3. 4 Busłowicz M.
  4. 3 Czornik A.
  5. 1 Abdelkrim Mohamed Naceur
Więcej...
Lata help
  1. 3 2023
  2. 3 2022
  3. 2 2021
  4. 1 2020
  5. 3 2019
Więcej...
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 55

Liczba wyników na stronie
first rewind previous Strona / 3 next fast forward last
Wyniki wyszukiwania
Wyszukiwano:
w słowach kluczowych:  układ liniowy
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 3 next fast forward last
1
Content available Fractional time-invariant compartmental linear systems
Kaczorek Tadeusz
International Journal of Applied Mathematics and Computer Science
|
2023
|
Vol. 33, no. 1
97--102
EN
Fractional time-invariant compartmental linear systems are introduced. Controllability and observability of these systems are analyzed. The eigenvalue assignment problem of compartmental linear systems is considered and illustrated with a numerical example.
2
Content available Transformations of the matrices of linear systems to their canonical form with desired eigenvalues
Kaczorek Tadeusz
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2023
|
Vol. 71, nr 6
art. no. e147342
EN
A new approach to the transformations of the matrices of linear continuous-time systems to their canonical forms with desired eigenvalues is proposed. Conditions for the existence of solutions to the problems were given and illustrated by simple numerical examples.
3
Content available Eigenvalues assignment in descriptor linear systems by state and its derivative feedbacks
Kaczorek Tadeusz
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2023
|
Vol. 71, nr 5
art. no. e145765
EN
The eigenvalues assignment problems for descriptor linear systems with state and its derivative feedbacks are considered herein. Necessary and sufficient conditions for the existence of solutions to the problems are established. The Euler and Tustin approximations of the continuous-time systems are analyzed. Procedures for computation of the feedbacks are given and illustrated by numerical examples.
4
Content available Some analysis problems of the linear systems
Kaczorek Tadeusz
Journal of Automation, Electronics and Electrical Engineering
|
2022
|
Vol. 4, No. 2
7--12
EN
New approaches to the transformations of the uncontrollable and unobservable matrices of linear systems to their canonical forms are proposed. It is shown that the uncontrollable pair (A,B) and unobservable pair (A,C) of linear systems can be transform to their controllable (𝐴̅ , 𝐵̅ ) and observable (𝐴̅ , 𝐶̅ ) canonical forms by suitable choice of nonsingular matrix M satisfying the condition 𝑀[𝐴 𝐵] = [𝐴̅ 𝐵̅ ] and [𝐴 𝐵]𝑀 = [𝐴̂ 𝐵̂ ], respectively. It is also shown that by suitable choice of the gain matrix K of the feedbacks of the derivative of the state vector it is possible to reduce the descriptor system to the standard one.
PL
Zaproponowano nowe podejścia do transformacji niesterowalnych i nieobserwowalnych macierzy układów liniowych do ich postaci kanonicznych. Wykazano, że niesterowalna para (A,B) i nieobserwowalna para (A,C) układów liniowych może być przekształcona do ich postaci kanonicznych sterowalnych i obserwowalnych prze odpowiedni dobór nieosobliwej macierzy M spełniającej warunki 𝑀[𝐴 𝐵] = [𝐴̅ 𝐵̅ ] i [𝐴 𝐵]𝑀 = [𝐴̂ 𝐵̂ ]. Pokazano,żeprzezodpowiednidobórmacierzyKsprzężeniazwrotnego od pochodnej wektora stanu jest możliwa redukcja układu deskryptorowegodoukładustandardowego.
5
Content available A Kalman filter with intermittent observations and reconstruction of data losses
Rhouma Taouba, Keller Jean-Yves, Abdelkrim Mohamed Naceur
International Journal of Applied Mathematics and Computer Science
|
2022
|
Vol. 32, no. 2
241--253
EN
This paper deals with the problem of joint state and unknown input estimation for stochastic discrete-time linear systems subject to intermittent unknown inputs on measurements. A Kalman filter approach is proposed for state prediction and intermittent unknown input reconstruction. The filter design is based on the minimization of the trace of the state estimation error covariance matrix under the constraint that the state prediction error is decoupled from active unknown inputs corrupting measurements at the current time. When the system is not strongly detectable, a sufficient stochastic stability condition on the mathematical expectation of the random state prediction errors covariance matrix is established in the case where the arrival binary sequences of unknown inputs follow independent random Bernoulli processes. When the intermittent unknown inputs on measurements represent intermittent observations, an illustrative example shows that the proposed filter corresponds to a Kalman filter with intermittent observations having the ability to generate a minimum variance unbiased prediction of measurement losses.
6
Content available Eigenvalues assignment in uncontrollable linear systems
Kaczorek Tadeusz
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2022
|
Vol. 70, nr 6
art. no. e141987
EN
It is shown that in uncontrollable linear system x = Ax + Bu it is possible to assign arbitrarily the eigenvalues of the closed-loop system with state feedbacks u = Kx, K ∈ ℜn⨉m if rank [A B] = n. The design procedure consists in two steps. In the step 1 a nonsingular matrix M ∈ ℜn⨉m is chosen so that the pair (MA,MB) is controllable. In step 2 the feedback matrix K is chosen so that the closed-loop matrix Ac = A − BK has the desired eigenvalues. The procedure is illustrated by simple example.
7
Content available Divisibility of the second-order minors of the nominators by minimal denominators of transfer matrices of cyclic fractional linear systems
Kaczorek Tadeusz
International Journal of Applied Mathematics and Computer Science
|
2021
|
Vol. 31, no. 4
627--633
EN
The divisibility of the second-order minors of the numerators of transfer matrices by their minimal denominators for cyclic fractional linear systems is analyzed. It is shown that all nonzero second-order minors of the numerators of the transfer matrices are divisible by their minimal denominators if and only if the system matrices of fractional standard and descriptor linear systems are cyclic. The theorems are illustrated by examples of fractional standard and descriptor linear systems.
8
Content available An interval Kalman filter enhanced by lowering the covariance matrix upper bound
Tran Tuan Anh, Jauberthie Carine, Trave-Massuyés Louise, Lu Quoc Hung
International Journal of Applied Mathematics and Computer Science
|
2021
|
Vol. 31, no. 2
259--269
EN
This paper proposes a variance upper bound based interval Kalman filter that enhances the interval Kalman filter based on the same principle proposed by Tran et al. (2017) for uncertain discrete time linear models. The systems under consideration are subject to bounded parameter uncertainties not only in the state and observation matrices, but also in the covariance matrices of the Gaussian noises. By using the spectral decomposition of a symmetric matrix and by optimizing the gain matrix of the proposed filter, we lower the minimal upper bound on the state estimation error covariance for all admissible uncertainties. This paper contributes with an improved algorithm that provides a less conservative error covariance upper bound than the approach proposed by Tran et al. (2017). The state estimates are determined using interval analysis in order to enclose the set of all possible solutions of the classical Kalman filter consistent with the uncertainties.
9
Content available Extremal properties of linear dynamic systems controlled by Dirac’s impulse
Białas Stanisław, Górecki Henryk, Zaczyk Mieczysław
International Journal of Applied Mathematics and Computer Science
|
2020
|
Vol. 30, no. 1
75--81
EN
The paper concerns the properties of linear dynamical systems described by linear differential equations, excited by the Dirac delta function. A differential equation of the form an x(n) (t) + ∙∙∙ a1 x’(t) + a0 x(t) = bm u (t) + ∙∙∙ + b1 u’(t) + b0 u(t) is considered with ai, bj >0. In the paper we assume that the polynomials Mn(s) = ansn + ∙∙∙ + a1s + a0 and Lm(s) = bmsm + ∙∙∙ + b1s + b0 partly interlace. The solution of the above equation is denoted by x(t, Lm, Mn). It is proved that the function x(t, Lm, Mn) is nonnegative for t ∊ (0, ∞) , and does not have more than one local extremum in the interval (0, ∞) (Theorems 1, 3 and 4). Besides, certain relationships are proved which occur between local extrema of the function x(t, Lm, Mn), depending on the degree of the polynomial Mn(s) or Lm(s) (Theorems 5 and 6).
10
Content available State estimators and observers for continuous and discrete linear systems. Part 2. Integral observers for exact state reconstruction
Byrski Jędrzej, Byrski Witold
Science, Technology and Innovation
|
2019
|
Vol. 5, no. 2
23--33
EN
In the paper, the exact state observers will be presented. The state estimators and observers can be used in technical processes for many purposes like the fault detection and diagnosis, the implementation of the state controllers, and soft reconstruction of inaccessible for measurements variables of the system. As the standard, for continuous systems the differential estimators of Kalman filter or Luenberger type observer are commonly used. However, if the initial conditions of the real state are unknown, both estimators guarantee only an asymptotic quality of the real state tracking. The paper presents another type of the state observers, which for continuous system have the structure given by two integral operators. Based on measurements of the system input and output signals on some predefined finite time interval T, they can reconstruct the initial state exactly. In on-line version, the exact state reconstruction is performed continuously for every t, based on special procedure executed within two moving windows of width T, on sliding time interval [t-T, t].
11
Content available The parallel tiled WZ factorization algorithm for multicore architectures
Bylina Beata, Bylina Jarosław
International Journal of Applied Mathematics and Computer Science
|
2019
|
Vol. 29, no. 2
407--419
EN
The aim of this paper is to investigate dense linear algebra algorithms on shared memory multicore architectures. The design and implementation of a parallel tiled WZ factorization algorithm which can fully exploit such architectures are presented. Three parallel implementations of the algorithm are studied. The first one relies only on exploiting multithreaded BLAS (basic linear algebra subprograms) operations. The second implementation, except for BLAS operations, employs the OpenMP standard to use the loop-level parallelism. The third implementation, except for BLAS operations, employs the OpenMP task directive with the depend clause. We report the computational performance and the speedup of the parallel tiled WZ factorization algorithm on shared memory multicore architectures for dense square diagonally dominant matrices. Then we compare our parallel implementations with the respective LU factorization from a vendor implemented LAPACK library. We also analyze the numerical accuracy. Two of our implementations can be achieved with near maximal theoretical speedup implied by Amdahl’s law.
12
Content available Event-based feedforward control of linear systems with input time-delay
Rodríguez Carlos, Aranda-Escolástico Ernesto, Guinaldo Maria, Guzmán José Luis, Dormido Sebastián
International Journal of Applied Mathematics and Computer Science
|
2019
|
Vol. 29, no. 3
541--553
EN
This paper proposes a new method for the analysis of continuous and periodic event-based state-feedback plus static feedforward controllers that regulate linear time invariant systems with time delays. Measurable disturbances are used in both the control law and triggering condition to provide better disturbance attenuation. Asymptotic stability and L2-gain disturbance rejection problems are addressed by means of Lyapunov–Krasovskii functionals, leading to performance conditions that are expressed in terms of linear matrix inequalities. The proposed controller offers better disturbance rejection and a reduction in the number of transmissions with respect to other robust event-triggered controllers in the literature.
13
Content available remote Normal positive linear systems and electrical circuits
Kaczorek T.
Przegląd Elektrotechniczny
|
2018
|
R. 94, nr 6
1--7
EN
The notion of normal positive electrical circuits is introduced and some their specific properties are investigated. New state matrices of positive linear systems and electrical circuits are proposed and their properties are analyzed. It is shown that positive electrical circuits with diagonal state matrices are normal for all values of resistances, inductances and capacitances.
PL
W artykule zaproponowano pojęcie dodatniego obwodu elektrycznego oraz przeanalizowano specjalne własności dodatnich układów i obwodów elektrycznych. Wykazano, że dodatnie obwody elektryczne z diagonalnymi macierzami stanu są zawsze normalne dla wszystkich wartości rezystancji, indukcyjności i pojemności.
14
Content available State filtering for networked control systems subject to switching disturbances
Chabir K., Rhouma T., Keller J. Y., Sauter D.
International Journal of Applied Mathematics and Computer Science
|
2018
|
Vol. 28, no. 3
473--482
EN
State estimation of stochastic discrete-time linear systems subject to unknown inputs has been widely studied, but few works take into account disturbances switching between unknown inputs and constant biases. We show that such disturbances affect a networked control system subject to deception attacks on the control signals transmitted by the controller to the plant via unreliable networks. This paper proposes to estimate the switching disturbance from an augmented state version of the intermittent unknown input Kalman filter. The sufficient stochastic stability conditions of the obtained filter are established when the arrival binary sequence of data losses follows a Bernoulli random process.
15
Content available Stability of interval positive fractional discrete-time linear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2018
|
Vol. 28, no. 3
451--456
EN
The aim of this work is to show that interval positive fractional discrete-time linear systems are asymptotically stable if and only if the respective lower and upper bound systems are asymptotically stable. The classical Kharitonov theorem is extended to interval positive fractional linear systems.
16
Content available Decentralized stabilization of fractional positive descriptor continuous-time linear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2018
|
Vol. 28, no. 1
135--140
EN
A method for decentralized stabilization of fractional positive descriptor linear systems is proposed. Necessary and sufficient conditions for decentralized stabilization of fractional positive descriptor linear systems are established. The efficiency of the proposed method is demonstrated on a numerical example.
17
Content available BIBO stabilisation of continuous-time Takagi–Sugeno systems under persistent perturbations and input saturation
Salcedo J. V., Martínez M., García-Nieto S., Hilario A.
International Journal of Applied Mathematics and Computer Science
|
2018
|
Vol. 28, no. 3
457--472
EN
This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi–Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.
18
Content available remote Responses of standard and fractional linear systems and electrical circuits with derivatives of their inputs
Kaczorek T.
Przegląd Elektrotechniczny
|
2017
|
R. 93, nr 6
132--136
EN
The responses of continuous-time and discrete-time linear systems with derivatives of their inputs are addressed. It is shown that the formulae for state vectors and outputs are also valid for their derivatives if the inputs and outputs and their derivatives of suitable order are zero for t = 0. Similar results are also shown for the discrete-time linear systems and for the fractional continuous-time and discrete-time linear systems.
PL
W artykule rozpatrywane są ciągłe układy i obwody elektryczne liniowe oraz dyskretne układy liniowe z pochodnymi (i odpowiednio różnicami) wymuszeń. Pokazano, że wzory określające pochodne wyjścia układów i wektorów stanu są również prawdziwe dla ich pochodnych jeżeli odpowiednie warunki początkowe i ich pochodnych są zerowe. Analogiczne wyniki zostały również wyprowadzone dla układów dyskretnych rzędów całkowitych i niecałkowitych.
19
Content available remote An Application of ΣΔ Undersampling to an Estimation of Linear System's Impulse Response
Nikołajew A.
Przegląd Elektrotechniczny
|
2016
|
R. 92, nr 2
75--77
EN
A method of a measurement of a linear system’s impulse response is presented. For a rectangular input signal ΣΔ undersampling of the system's output signal enables calculations of its impulse response. An algorithm of output signal's digital processing enabling a reduction of errors is described. A dependence of measurement's errors on the number of samples per period and relation between sampling and signal's frequencies was analyzed. Exemplary calculations were performed for two typical linear systems.
PL
Zaprezentowano metodę pomiaru odpowiedzi impulsowej układu liniowego wykorzystującą podpróbkowanie ΣΔ jego sygnału wyjściowego przy prostokątnym sygnale wejściowym. Przedstawiono algorytm przetwarzania sygnałów, umożliwiający redukcję błędów pomiarowych. Przeanalizowano zależność błędów od krotności podpróbkowania, liczby próbek oraz błędów częstotliwości na przykładzie 2 typowych układów liniowych.
20
Content available Fractional descriptor continuous-time linear systems described by the Caputo–Fabrizio derivative
Kaczorek T., Borawski K.
International Journal of Applied Mathematics and Computer Science
|
2016
|
Vol. 26, no. 3
533--541
EN
The Weierstrass–Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor continuous-time linear systems described by the Caputo–Fabrizio derivative. A method for computing solutions of continuous-time systems is presented. Necessary and sufficient conditions for the positivity and stability of these systems are established. The discussion is illustrated with a numerical example.
first rewind previous Strona / 3 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.