Stability Analysis of Networked Sampled-Data Linear Systems With Markovian Packet Losses

We consider the stability properties of sampled-data networked linear systems with Markovian packet losses. A binary Markov chain is used to characterize the packet loss phenomenon of the network. We show that the sampled-data system under consideration can be considered as a randomly sampled system with an i.i.d. random sampling period. Necessary and sufficient conditions for the stochastic stability properties are established. Those conditions are based on the relationships of stability properties between the systems evolving in deterministic continuous time, deterministic discrete time, and random discrete time. In addition, the asymptotic stability of the system is also studied by using Lyapunov exponent method.