H∞ Control for LPV Discrete Systems with Random Time-Varying Network Delay

In this paper, we study the H∞ control problem for Linear Parameter Varying (LPV) discrete systems with random time-varying network delay. The state matrices of LPV discrete systems are deterministic functions and changed with parameters; the range of parameters is measurable. Considering the characteristics of networks with random time-varying delay, we proposed a new parameter-dependent H∞ performance criterion based on the Lyapunov stability theory. The coupling between Lyapunov functions and system matrices could be eliminated by introducing an additional matrix in this criterion, which made it easier for numerical implementation. On this basis, we designed a state feedback controller by virtue of linear matrix inequalities, which transformed the sufficient conditions into existence condition of solution of parametric linear matrix inequalities. The designed controller could keep the closed-loop system asymptotically stable under given time delay and probability and meet predefined performance metric. The validity of the proposed method is verified by numerical simulation