Stability of discrete-time time-varying linear systems with Markov perturbations in Hilbert spaces
by
Viorica Mariela Ungureanu
Department of Mathematics, Constantin Brancusi University, Tg-Jiu, Romania

We investigate the stability problem for a class of discrete-time time-varying linear systems with Markov perturbations in real separable Hilbert spaces. We give a representation of the mean square of the solution of the stochastic system by using the solutions of a linear discrete-time system in a Banach space. Consequently, the stability problem for the stochastic system reduces to a similar one for the associated discrete-time system. The study of the properties of the associated discrete-time system lead us to the conclusion that the stochastic stability problem is closely related to the existence of a unique, global, uniformly positive and bounded solution of a Lyapunov - type equation defined on an ordered Banach space.

Date received: April 20, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caun-11.