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1
Content available Stability of convex linear combinations of continuous-time and discrete-time linear systems
Kaczorek Tadeusz
Archives of Control Sciences
|
2023
|
Vol. 33, No. 4
789--799
EN
The asymptotic stability of the convex linear combination of continuous-time and discrete-time linear systems is considered. Using the Gershgorin theorem it is shown that the convex linear combination of the linear asymptotically stable continuous-time and discretetime linear systems is also asymptotically stable. It is shown that the above thesis is also valid (even simpler) for positive linear systems.
2
Content available New stability tests for fractional positive descriptor linear systems
Kaczorek Tadeusz, Ruszewski Andrzej
Archives of Control Sciences
|
2023
|
Vol. 33, No. 1
71--81
EN
The asymptotic stability of fractional positive descriptor continuous-time and discrete-time linear systems is considered. New sufficient conditions for stability of fractional positive descriptor linear systems are established. The efficiency of the new stability conditions are demonstrated on numerical examples of fractional continuous-time and discrete-time linear systems.
3
Content available Standard and fractional discrete-time linear systems with zero transfer matrices
Kaczorek Tadeusz, Ruszewski Andrzej
Acta Mechanica et Automatica
|
2023
|
Vol. 17, no. 2
188--191
EN
The transfer matrix of the standard and fractional linear discrete-time linear systems is investigated. Necessary and sufficient conditions for zeroing of the transfer matrix of the linear discrete-time systems are established. The considerations are illustrated by examples of the standard and fractional linear discrete-time systems.
4
Content available New stability tests for positive descriptor linear systems
Kaczorek Tadeusz
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2022
|
Vol. 70, nr 3
art. no. e140688
EN
The asymptotic stability of positive descriptor continuous-time and discrete-time linear systems is considered. New sufficient conditions for stability of positive descriptor linear systems are established. The efficiency of the new stability conditions are demonstrated on numerical examples of continuous-time and discrete-time linear systems.
5
Content available Exponential decay of transient values in discrete-time positive nonlinear systems
Kaczorek Tadeusz, Ruszewski Andrzej
Archives of Control Sciences
|
2022
|
Vol. 32, No. 3
577--588
EN
The exponential decay of transient values in discrete-time nonlinear standard and fractional orders systems with linear positive linear part and positive feedbacks is investigated. Sufficient conditions for the exponential decay of transient values in this class of positive nonlinear systems are established. A procedure for computation of gains characterizing the class of nonlinear elements are given and illustrated on simple example.
6
Content available A new method for computation of positive realizations of linear discrete-time systems
Kaczorek Tadeusz
Journal of Automation Mobile Robotics and Intelligent Systems
|
2021
|
Vol. 15, No. 1
3--8
EN
A new method for computation of positive realizations of given transfer matrices of linear discretetime linear systems is proposed. Sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by an example.
7
Content available Global stability of positive discrete-time time-varying nonlinear feedback systems
Kaczorek Tadeusz, Sajewski Łukasz
Journal of Automation, Electronics and Electrical Engineering
|
2021
|
Vol. 3, No. 1
17--20
EN
The global stability of positive discrete-time time-varying nonlinear systems with time-varying scalar feedbacks is investigated. Sufficient conditions for the asymptotic stability of discrete-time positive time-varying linear systems are given. The new conditions are applied to discrete-time positive time-varying nonlinear systems with time-varying feedbacks. Sufficient conditions are established for the global stability of the discrete-time positive time-varying nonlinear systems with feedbacks.
8
Content available Application of the Lagrange-Sylvester formula to computation of the solution to state equations of fractional linear systems
Kaczorek Tadeusz
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2021
|
Vol. 69, nr 2
art. no. e136729
EN
The Lagrange-Sylvester formula is applied to the computation of the solutions of state equations of fractional continuous-time and discrete-time linear systems. The solutions are given as finite sums with their numbers of components equal to the degrees of the minimal characteristics polynomials of state matrices of the systems. Procedures for computations of the solutions are given and illustrated by numerical examples of continuous-time and discrete-time fractional linear systems.
9
Content available The pointwise completeness and the pointwise degeneracy of linear discrete-time different fractional order systems
Kaczorek T., Sajewski Ł.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2020
|
Vol. 68, nr 6
1513--1516
EN
Necessary and sufficient conditions for the pointwise completeness and the pointwise degeneracy of linear discrete-time different fractional order systems are established. It is shown that if the fractional system is pointwise complete in one step (q = 1), then it is also pointwise complete for q = 2, 3…
10
Content available Global stability of discrete-time nonlinear systems with descriptor standard and fractional positive linear parts and scalar feedbacks
Kaczorek T., Ruszewski A.
Archives of Control Sciences
|
2020
|
Vol. 30, No. 4
667--681
EN
The global stability of discrete-time nonlinear systems with descriptor positive linear parts and positive scalar feedbacks is addressed. Sufficient conditions for the global stability of standard and fractional nonlinear systems are established. The effectiveness of these conditions is illustrated on numerical examples.
11
Content available Exact determinantions of maximal output admissible set for a class of semilinear discrete systems
El Bhih Amine, Benfatah Youssef, Rachik Mostafa
Archives of Control Sciences
|
2020
|
Vol. 30, No. 3
523--552
EN
Consider the semilinear system defined by {x(i+1)=Ax(i)+f(x(i)), i≥0 x(0)=x0∈Rn and the corresponding output signal y(i)=C x(i), i≥0, where A is a n×n matrix, C is a p x n matrix and f is a nonlinear function. An initial state x(0) is output admissible with respect to A, f, C and a constraint set Ω ⊂ Rp, if the output signal (y(i)i associated to our system satisfies the condition y(i) ∈ Ω, for every integer i≥0. The set of all possible such initial conditions is the maximal output admissible set Γ(Ω). In this paper we will define a new set that characterizes the maximal output set in various systems(controlled and uncontrolled systems) .Therefore, we propose an algorithmic approach that permits to verify if such set is finitely determined or not. The case of discrete delayed systems is taken into consideration as well. To illustrate our work, we give various numerical simulations.
12
Content available Practical and asymptotic stabilities for a class of delayed fractional discrete-time linear systems
Ruszewski A.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2019
|
Vol. 67, nr 3
509--515
EN
The practical and asymptotic stabilities of delayed fractional discrete-time linear systems described by the model without a time shift in the difference are addressed. The D-decomposition approach is used for stability analysis. New necessary and sufficient stability conditions are established. The conditions in terms of the location of eigenvalues of the system matrix in the complex plane are given.
13
Content available Stability of discrete-time fractional linear systems with delays
Ruszewski Andrzej
Archives of Control Sciences
|
2019
|
Vol. 29, No. 3
549--567
EN
The stability analysis for discrete-time fractional linear systems with delays is presented. The state-space model with a time shift in the difference is considered. Necessary and sufficient conditions for practical stability and for asymptotic stability have been established. The systems with only one matrix occurring in the state equation at a delayed moment have been also considered. In this case analytical conditions for asymptotic stability have been given. Moreover parametric descriptions of the boundary of practical stability and asymptotic stability regions have been presented.
14
Content available Absolute stability of a class of positive nonlinear continuous-time and discrete-time systems
Kaczorek Tadeusz
Archives of Control Sciences
|
2019
|
Vol. 29, No. 1
157--167
EN
The positivity and absolute stability of a class of nonlinear continuous-time and discrete-time systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of nonlinear systems are also given.
15
Content available Absolute stability of a class of nonlinear systems with nonpositive linear parts
Kaczorek Tadeusz
Archives of Control Sciences
|
2019
|
Vol. 29, No. 2
247--258
EN
The positivity and absolute stability of a class of nonlinear continuous-time and discrete-time systems with nonpositive linear part are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of nonlinear systems are also given.
16
Content available Responses of positive standard and fractional linear systems and electrical circuits with derivatives of their inputs
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2018
|
Vol. 66, nr 4
419--425
EN
Responses of positive standard and fractional continuous-time and discrete-time linear systems with derivatives of their inputs are presented herein. 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 positive standard and fractional discrete-time linear systems.
17
Content available Reachability and observability of positive discrete-time linear systems with integer positive and negative powers of the state Frobenius matrices
Kaczorek T.
Archives of Control Sciences
|
2018
|
Vol. 28, No. 1
119--133
EN
The notions of monomial generalized Frobenius matrices is proposed and the reachability and observability of positive discrete-time linear systems with positive and negative integer powers of the state matrices is addressed. Necessary and sufficient conditions for the reachability of the positive systems are established.
18
Content available An extension of Klamka’s method to positive descriptor discrete-time linear systems with bounded inputs
Kaczorek T.
Archives of Control Sciences
|
2018
|
Vol. 28, No. 2
255--268
EN
The minimum energy control problem for the positive descriptor discrete-time linear systems with bounded inputs by the use of Weierstrass-Kronecker decomposition is formulated and solved. Necessary and sufficient conditions for the positivity and reachability of descriptor discrete-time linear systems are given. Conditions for the existence of solution and procedure for computation of optimal input and the minimal value of the performance index is proposed and illustrated by a numerical example.
19
Content available Relationship between the observability of standard and fractional linear systems
Kaczorek T.
Archives of Control Sciences
|
2017
|
Vol. 27, no. 3
441--451
EN
The relationship between the observability of standard and fractional discrete-time and continuous-time linear systems are addressed. It is shown that the fractional discrete-time and continuous-time linear systems are observable if and only if the standard discrete-time and continuous-time linear systems are observable.
20
Content available Synteza obserwatora pełnego rzędu singularnych układów dyskretnych niecałkowitego rzędu
Kociszewski R.
Pomiary Automatyka Robotyka
|
2016
|
R. 20, nr 4
9--13
PL
W pracy rozpatrzono zagadnienie syntezy obserwatora pełnego rzędu dla układów liniowych dyskretnych singularnych niecałkowitego rzędu. Sformułowano analityczne kryteria istnienia obserwatora i podano sposób wyznaczania macierzy wzmocnień obserwatora. Rozważania teoretyczne, do których wykorzystano liniowe nierówności macierzowe (LMI) zilustrowano przykładem liczbowym.
EN
The paper is devoted to observer synthesis for linear singular discrete-time fractional systems. The problem of finding a nonnegative gain matrix of the observer such that the observer is asymptotically stable is formulated and solved by the use of linear matrix inequality (LMI) method. The proposed approach to the observer synthesis is illustrated by theoretical example.
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