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

Kewang Huang,Feng Pan,Tao Ma

doi:10.1155/2018/9095014

Abstract

In this paper, we study theH∞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-dependentH∞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.

Highlights

In recent years, the gain scheduling control has become one of the most effective methods in nonlinear control domains, and the application of gain scheduling control based on Linear Parameter-Varying (LPV) system is boosting
We study the H∞ control problem for Linear Parameter Varying (LPV) discrete systems with random time-varying network delay
Where 1 ≤ dm ≤ d(k) ≤ dM and K(ρ) ∈ Rp×n represents the unknown gain matrix of state feedback controller, which depends on parameter vector ρ(k), d(k) represents the random time-varying network delay. dm and dM represent the lower and upper bound of time delay, respectively. δk represents whether a delay will occur or not when the signal is transmitted from the sensor to the controller through network channel

Summary

Introduction

The gain scheduling control has become one of the most effective methods in nonlinear control domains, and the application of gain scheduling control based on Linear Parameter-Varying (LPV) system is boosting. Faiz & Sing [20] and Luan & Shi & Liu [21] researched the stability problems of networked control system with random time delay. They proposed the Mathematical Problems in Engineering design of controller with random time delay, which will keep the closed-loop system asymptotically stable. H∞ control problem of LPV discrete systems with random time-varying network delay is still an open problem. The investigation of these systems has practical reference value and realistic signification. We investigate the above-mentioned LPV discrete systems with random time-varying network delay in this paper.

Problem Formulation

Main Theorems

Numerical Simulations

Conclusion