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

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