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1
Content available New stability tests for positive descriptor linear systems
Kaczorek Tadeusz
Bulletin of the Polish Academy of Sciences. Technical Sciences
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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.
2
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.
3
Content available Stability of fractional positive continuous-time linear systems with state matrices in integer and rational powers
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2017
|
Vol. 65, nr 3
305--311
EN
The stability of fractional standard and positive continuous-time linear systems with state matrices in integer and rational powers is addressed. It is shown that the fractional systems are asymptotically stable if and only if the eigenvalues of the state matrices satisfy some conditions imposed on the phases of the eigenvalues. The fractional standard systems are unstable if the state matrices have at least one positive eigenvalue.
4
Content available Pointwise completeness and pointwise degeneracy of fractional descriptor continuous-time linear systems with regular pencils
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2015
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Vol. 63, nr 1
169-–172
EN
Pointwise completeness and pointwise degeneracy of the fractional descriptor continuous-time linear systems with regular pencils are addressed. Conditions for the pointwise completeness and pointwise degeneracy of the systems are established and illustrated by an example.
5
Content available Minimum energy control of positive time-varying linear systems
Kaczorek T.
Acta Mechanica et Automatica
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2015
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Vol. 9, no. 4
225--228
EN
The minimum energy control problem for the positive time-varying linear systems is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by a numerical example.
6
Content available remote Robust stability of positive continuous-time linear systems with delays
Busłowicz M.
International Journal of Applied Mathematics and Computer Science
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2010
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Vol. 20, no 4
665-670
EN
The paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.
7
Content available remote Generalizations of the Cayley-Hamilton theorem with applications
Kaczorek T.
Archives of Electrical Engineering
|
2007
|
Vol. 56, nr 1
3-41
EN
New generalizations of the classical Cayley-Hamilton theorem for rectangular matrices, block matrices, matrices depending on parameters, discrete-time and continuous-time systems with delays, polynomial matrices with commuting matrices, n-D polynomial matrices, singular systems, right and left inverse of polynomial matrices, rational matrices, impulse response matrices and nonlinear time-varying systems are presented. Some applications of the generalizations and illustrating examples are also given.
PL
W pracy podano nowe uogólnienia klasycznego twierdzenia Cayley-Hamiltona na: macierze prostokątne, macierze blokowe, macierze zależne od parametrów, macierze układów ciągłych i dyskretnych z opóźnieniami, macierze wielomianowe z macierzami przemiennymi, macierze wielomianowe o elementach będącymi funkcjami n zmiennych, macierze układów singularnych, prawe i lewe odwrotności macierzy wielomianowych, macierze wymierne, macierze odpowiedzi impulsowych oraz na macierze układów nieliniowych o parametrach zmiennych w czasie. Podano również pewne zastosowania tych uogólnień twierdzenia Cayley-Hamiltona. Rozważania zostały zilustrowane przykładami.
8
Content available remote A realization problem for positive continuous-time systems with reduced numbers of delays
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2006
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Vol. 16, no 3
325-331
EN
A realization problem for positive, continuous-time linear systems with reduced numbers of delays in state and in control is formulated and solved. Sufficient conditions for the existence of positive realizations with reduced numbers of delays of a given proper transfer function are established. A procedure for the computation of positive realizations with reduced numbers of delays is presented and illustrated by an example.
9
Content available remote Extension of The Cayley-Hamilton Theorem to Continuous-time Linear Systems With Delays
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2005
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Vol. 15, no 2
231-234
EN
The classical Cayley-Hamilton theorem is extended to continuous-time linear systems with delays. The matrices $A_0, A_1, dots, A_h in R^{n times n}$ of the system with $h$ delays $dot xleft(t right) = A_0 xleft(t right) + sum_{i = 1}^h {A_i xleft( {t - hi} right) + Buleft( t right)}$ satisfy $nh + 1$ algebraic matrix equations with coefficients of the characteristic polynomial $pleft( {s,w}right) = det left[ {I_n s - A_0 - A_1 w - cdots - A_h w^h }right]$, $w = e^{- hs}$.
10
Content available remote Identification of Low-Order Continuous-Time Models Via Discrete-Time Trends of Measurements
Janiszowski K. B.
International Journal of Applied Mathematics and Computer Science
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1999
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Vol. 9, no 4
839-853
EN
The paper deals with the problem of continuous-time (CT) identification of parameters in transfer functions for low-order linear systems, based on recorded discrete-time (DT) data. Algorithms for direct estimation of CT parameters are developed from rules for transformation of a CT transferfunction controlled via a zero-order sampling-and-hold unit into a DT representation.Two schemes are derived and tested: the first is based on the Goodwin transformation and the other is derived from the modified Tustin transformation. Both the approaches result in relations which can be used for direct estimationof CT parameters in a model of the investigated system. The numerical schemes contain some expressions that are reminiscent of DT differences and consequently they may magnify disturbances. Therefore the results of extensively testing both the schemes including different types of disturbances, measurement noise, slow varying drifts, measurement resolution errors together with changes in the sampling time are presented. A model of a pneumatic servomechanism system was used as a test plant.
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