Stochastic stability for model-based networked control systems

Abstract

In this paper we study the stochastic stability properties of certain networked control system. Specifically we study the stability of the model-based network control system introduced in [L.A. Montestruque et. al., 41st IEEE Conference on Decision and Control, December 2002.] under time-varying communication. The model-based network control system uses knowledge of the plant to reduce the number of packet exchanges and thus the network traffic. Stability conditions for constant data packet exchange rates are analysed in [L.A. Montestruque et. al., 41st IEEE Conference on Decision and Control, December 2002, L.A. Montestruque et.al., ISIS Technical Report ISIS-2002-001, January 2001]. Here we concentrate on the stochastic stability of the networked system when the packet exchange times are time varying and have some known statistical properties. Conditions are derived for almost sure and mean square stability for independent, identically distributed update times. Mean square stability is also studied for Markov chain driven update times.