Stability of discrete descriptive time delayed system in the sense of Lyapunov

Abstract

This paper gives sufficient conditions for the stability of linear descriptor discrete delay systems of the particular form. These new, delay-independent sufficient conditions are derived using approach based on Lyapunov's direct method. This paper, for the first time, offers a general case in the sense that necessity for regularity of system basic matrix A0 is not any more required what was a general assumption in already existing results in literature. The presented method is a typical geometric approach to the problem exposed and avoids needs to transform then system under consideration into the classical discrete descriptor system. In that sense one is capable to see how much should be matrix 0 A stable to overcome instability caused by the time delay matrix 1 A . Numerical example has been working out to show the applicability of results derived.Index Terms-Descriptor time delayed systems, Asymptotic stability, Lyapunov second method I.

The one-step-map for switched singular systems in discrete-time

“…The following lemma (without proof) highlights a simple geometric property of subspaces and will be crucial for deriving the upcoming explicit solution formula for (8). Lemma 3.4:…”

“…In what follows we give a constructive formula for the matrix Φ i,j as well as for the unique solution of SwSS (8).…”