Improved Mode-Dependent State-Feedback Stabilization of Discrete-Time Networked Control Systems with Markovian Communication Delays

Abstract

The modeling issues in dynamical systems in many processes, networked control systems (NCS) are very complex. The models may contain subsystems with different parameters, which arise when using a network in an NCS such as time delay, limited bandwidth, and so on. Controlling these types of multiple time delay system is challenging, due to mathematical complexity. This paper considers the design of a stabilizing state-feedback controller for a networked control system with random communication delays. Sensor-to-controller (S-C) and controller-to-actuator delays are modeled by two independent Markov chains. Network-induced random delays are modeled as a Markov chain, and the resulting closed-loop system is transformed into a Markovian jump linear system (MJLS). The focus is on the design of a controller that fully incorporates the effect of the C-A delay. The resulting closed-loop system is described by a new discrete-time Markovian jump linear system with Markov delays model. Then, by applying a type of stochastic Lyapunov functional, sufficient conditions on the stochastic stabilizability and the existence of controller are derived in terms of coupled linear matrix inequalities (LMIs). The efficacy of the proposed method is shown through illustrative examples. Simulation results demonstrate the applicability and the effectiveness of the obtained theoretical results.