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Archives of Electrical Engineering
2013 Vol. 62, nr 2 345--355
EN The positive asymptotically stable continuous-time linear systems are approximated by corresponding asymptotically stable discrete-time linear systems. Two methods of the approximation are presented and the comparison of the methods is addressed. The considerations are illustrated by three numerical[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
EN Models of singular compartmental linear continuous-time and discrete-time systems are introduced. Solutions of the singular models in terms of the Drazin inverse of the models matrices are given. Necessary and sufficient conditions for the singular systems to be compartmental are established. A noti[...]
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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 [...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
EN In the paper the problems of practical stability and asymptotic stability of fractional discrete-time linear systems with a diagonal state matrix are addressed. Standard and positive systems are considered. Simple necessary and sufficient analytic conditions for practical stability and for asymptoti[...]
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Journal of Automation Mobile Robotics and Intelligent Systems
EN Simple new necessary and sufficient conditions for robust stability of the positive linear discrete-time systems with one delay in the general case and in the two special cases: 1) linear unity rank uncertainty structure, 2) linear uncertainty structure with non-negative perturbation matrices, are [...]
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Archives of Control Sciences
EN A new test for checking the reachability (observability) of positive discrete-time linear systems is proposed. Conditions are established under which the unreachable pair (A;B) and the unobservable pair (A;C) of positive discrete-time system can be decomposed into reachable and unreachable parts and[...]
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Archives of Control Sciences
2013 Vol. 23, no. 2 205--211
EN The minimum energy control problem for the positive discrete-time linear systems with bounded inputs 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[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
2013 Vol. 61, nr 4 779--786
EN In the paper the problems of practical stability and asymptotic stability of fractional discrete-time linear systems are addressed. Necessary and sufficient conditions for practical stability and for asymptotic stability are established. The conditions are given in terms of eigenvalues of the state [...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
EN The minimum energy control problem for the positive discrete-time linear systems with bounded inputs is formulated and solved. Necessary and 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 num[...]
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Logistyka
PL W pracy zaproponowano nowe kryteria badania osiągalności (obserwowalności) dodatnich liniowych układów dyskretnych. Podano warunki przy spełnieniu których para nieosiągalna (A,B) oraz para nieobserwowalna (A,C) dodatniego układu dyskretnego może być zdekomponowana na część osiągalna i nieosiągalną o[...]
EN A new test for checking the reachability (observability) of positive discrete-time linear systems is proposed. Conditions are established under which the unreachable pair (A,B) and the unobservable pair (A,C) of positive discrete-time system can be decomposed into reachable and unreachable parts and[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
EN A new class of positive fractional 2D hybrid linear systems is introduced. The solution of the hybrid system is derived. The classical Cayley-Hamilton theorem is extended for fractional 2D hybrid systems. Necessary and sufficient conditions for the positivity are established.
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Archives of Control Sciences
EN The positive linear fractional discrete-time Lyapunov systems are introduced. The necessary and sufficient conditions for the positivity, reachability, controllability to zero and observability of the systems are established. The sufficient conditions for stability are given. The notion of the dual [...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
EN Simple new necessary and sufficient conditions for asymptotic stability of the positive linear discrete-time systems with delays in states are established. It is shown that asymptotic stability of the system is equivalent to asymptotic stability of the corresponding positive discrete-time system wit[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
EN A new concept (notion) of the practical stability of positive fractional discrete-time linear systems is introduced. Necessary and sufficient conditions for the practical stability of the positive fractional systems are established. It is shown that the positive fractional systems are practically un[...]
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Archives of Control Sciences
EN The notion of output-rezchability is extended for positive linear discrete-time systems with delays described by the stste equations, by the transfer matrices and by the impulse matrices. Necessary and sufficient conditions for the output-reachability are established. The calssical Cayley-Hamilton t[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
EN New tests (criterions) for checking the reachability and the observability of positive linear-discrete-time systems are proposed. The tests do not need checking of Tank conditions of the reachability and observability matrices of the systems. Simple sufficient conditions for the unreachability and u[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
EN Simple necessary and sufficient conditions for robust stability of the positive linear discrete-time systems wit h delays with linear uncertainty structure in two cases: 1) unity rank uncertainty structure, 2) non-negative perturbation matrices, are established. The proposed condi-tions are compared[...]
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Systems Science
EN The concept of maintainability for (time-invariant) positive linear discrete-time systems (PLDS) is introduced and studied in detail. A state x(t) of a PLDS is said to be maintainable if there exists an admissible control such that x(t + 1) = x(t) for t = 0, 1, 2, ... For time-invariant systems, if [...]
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Archives of Control Sciences
EN Necessary and sufficient conditions for the positivity of descriptor continuous-time and discrete-time linear systems are established. The shuffle algorithm is applied to transform the state equations of the descriptor systems to their equivalent form for which necessary and sufficient conditions fo[...]
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Archives of Control Sciences
EN The problem of computation of initial conditions and inputs for given outputs of fractional standard and positive discrete-time linear systems is formulated and solved. Necessary and sufficient conditions for existence of solution to the problem are established. It is shown that there exist the uniq[...]
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