Design for networked control systems with compound Markovian transition probabilities

This paper is concerned with stability and controller design of networked control systems (NCSs) with a compound Markovian transition probabilities. Firstly, a compound Markovian transition probabilities matrix is defined to described the work process of NCSs and co-decided by two independent work process: one is the packet dropouts process, which is defined as the sequence of the time intervals between consecutively successfully transmitted data; The other is the network-induced delay process, which is related to the delay of successfully transmitted data and based on a random division of intervals. Moreover, a new hybrid Markovian jump nonlinear systems (HMJNSs) model for NCSs is proposed. For handling the inter-sample behavior, which leads to nonlinear in model, anew norm bounded method is proposed. Furthermore, based on the such method and an operative mode dependent Lyapunov functional, sufficient conditions for mean square stability are derived in the form of linear matrix inequalities (LMIs) and corresponding control laws are given. Finally, numerical example illustrates the effectiveness of the results.