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A new D-stability area for linear discrete-time systems

Krokavec Dušan, Filasová Anna

Archives of Control Sciences

2019

Vol. 29, No. 1

5--23

The paper addresses the problem of constrained pole placement in discrete-time linear systems. The design conditions are outlined in terms of linear matrix in equalities for the D-stable ellipse region in the complex Z plain. In addition, it is demonstrated that the D-stable circle region formulation is the special case of by this way formulated and solved pole placement problem. The proposed principle is enhanced for discrete-time linear systems with polytopic uncertainties.

The selected problems of controllability of discrete-time switched linear systems with constrained switching rule

Babiarz A., Czornik A., Klamka J., Niezabitowski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2015

Vol. 63, nr 3

657--666

In this paper the controllability problem for discrete-time linear switched systems is considered. The main goal is to find a control signal that steers any initial state to a given final state independently of the switching signal. In the paper, it is assumed that there are some constraints posed on the switching signal. Moreover, we present a necessary and sufficient conditions of some kinds of controllability. Three types of controllability, namely: from zero initial state to any final state, from any initial state to zero final state and from any initial state to any final state are considered. Finally, three illustrative examples are shown.

Comparison of approximation methods of positive stable continuous-time linear systems by positive stable discrete-time systems

Kaczorek T.

Poznan University of Technology Academic Journals. Electrical Engineering

2013

No. 73

9--20

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 examples and an example of positive electrical circuit.

Feedback and positive feedback holdability of discrete-time systems.

Rumchev VG.

Systems Science

2000

Vol. 26, nr 3

15-23

We consider the following problems. Given a discrete-time linear system, find, if possible, linear state-feedback control laws such that the corresponding closed-loop system trajectory is positive whenever the initial state is positive. This problem is called the feedback holdability problem. If, in addition, the requirement of non-negativity is imposed on controls, the problem is a positive feedback holdability problem. In the paper, necessary and sufficient conditions for feedback and positive feedback holdability are established in a form of systems of linear inequalities and a procedure for computing the set of all state-feedback controllers that make the closed-loop system holdable is proposed. The relation between controllability and holdability is also treated. Feedback and positive feedback holdability of the class of positive systems is considered as well.