Stochastic Stability Analysis and Control of Networked Control Systems with Multiple Markovian Processes

Abstract

A novel stochastic system model with multiple Markovian processes for networkedcontrol system (NCS) is developed as a two chains Markovian jump linear system.By using an active sampling method, random time delays are reshaped into shorttime delays which are less than one sampling period such that the structure ofthe augmented discrete-time model becomes straightforward. Based on Lyapunovapproach, sufficient conditions for the stochastic stability of the networkedcontrol system are derived and mode-dependent controller is designed in termsof linear matrix inequalities (LMIs) to overcome the adverse influences of stochastictime delays and packet dropouts encountered in network-based distributedreal-time control. Gridding approach is introduced to guarantee the solvabilityof the LMIs with finite jump modes. A numerical example is given to illustratethe effectiveness of the proposed method.