Stability analysis and stabilization of networked linear systems with random packet losses

This paper is concerned with the stability analysis and stabilization of networked discrete-time and sampled-data linear systems with random packet losses. Asymptotic stability, mean-square stability, and stochastic stability are considered. For networked discrete-time linear systems, the packet loss period is assumed to be a finite-state Markov chain. We establish that the mean-square stability of a related discrete-time system which evolves in random time implies the mean-square stability of the system in deterministic time by using the equivalence of stability properties of Markovian jump linear systems in random time. We also establish the equivalence of asymptotic stability for the systems in deterministic discrete time and in random time. For networked sampled-data systems, a binary Markov chain is used to characterize the packet loss phenomenon of the network. In this case, the packet loss period between two transmission instants is driven by an identically independently distributed sequence assuming any positive values. Two approaches, namely the Markov jump linear system approach and randomly sampled system approach, are introduced. Based on the stability results derived, we present methods for stabilization of networked sampled-data systems in terms of matrix inequalities. Numerical examples are given to illustrate the design methods of stabilizing controllers.