Stability analysis and controller design for networked control systems with random time delay

This paper deals with the problem of stabilization for a class of networked control systems (NCSs) with random time delay via the state feedback control. The transmission delay is modeled as a Markov process, and the resulting closed-loop system is modeled as a Markovian jump linear system (MJLS). Based on Lyapunov stability theorem combined with linear matrix inequalities (LMIs) techniques, A new delay-dependent stochastic stability criterion for the system is derived. A state feedback controller that makes the closed-loop system stochastically stable is designed, which is obtained by solving some linear matrix inequalities. Numerical simulation result illustrates the effectiveness of the method proposed in this paper.

I. Introduction

Feedback control systems in which the control loops are closed through a real-time network are called networked control systems (NCSs). Recently, much attention has been paid to the study of stability analysis and control design of networked control systems (NCSs) [1]–[3] due to their low cost, reduced weight and power requirements, simple installation and maintenance, and high reliability. However, since the sampling data and controller signals are transmitted through a network, network-induced delays and date dropout in NCSs are always inevitable, see [4]–[5]. One of the main issues in NCSs is network-induced delays, which are usually the major causes for the deterioration of system dynamic performance and potential system instability, see [6]. For different scheduling protocols, the network-induced delay may be constant, time-varying or random variable [7].