Linear Matrix Inequality Approach to Stochastic Stabilization of Networked Control System with Markovian Jumping Parameters

This paper is concerned with the stochastic stabilization problem for a class of networked control system (NCS) with destabilizing transmission factors. By introducing the effective sampling instant to model random time delays and successive packet dropouts as two independent Markov chains, NCS is modeled as a discrete-time Markovian jump linear system with mixed integrated Markovian jumping parameters. In this way, a novel framework to analyze the stochastic stabilization problem of NCS is provided. The necessary and sufficient conditions for the stochastic stabilization of the NCS are obtained by the Lyapunov method and the state-feedback controller gain that depends on the delay modes is obtained in terms of the linear matrix inequalities (LMIs) formulation via the Schur complement theory. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.