Robust Preview Control for Uncertain Discrete Singular Systems

Jiang Wu,Shujie Gao,Hao Wang,Fucheng Liao,Zhengguang Xu,Yifan Shao

doi:10.1155/2018/1096793

Jiang Wu, Shujie Gao + Show 4 more

Open Access

https://doi.org/10.1155/2018/1096793

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Abstract

In this paper, the problem of robust preview control for uncertain discrete singular systems is considered. First of all, by employing the forward difference for uncertain discrete singular systems, the singular augmented error system with the state vector, the input control vector, and the previewable reference signal is derived. Since there is a singular matrix in the system, the existing method cannot be directly applied to this problem. By considering the stability of the transposition system with Linear Matrix Inequality (LMI) method, a new stability criterion for the transposition system is introduced. Then, the robust controller for the augmented error system is obtained, which is regarded as the robust preview controller for the original singular system. At last, the numerical simulation shows the correctness and effectiveness of the results.

Highlights

Since the singular system model [1] is proposed by Rosenbrock in the early 1970s, the singular system has been widely studied, and many results are obtained [2, 3]
Because of the existence of the singular matrix, a proper Lyapunov function cannot be found by the current method to design the robust preview controller
Since the two unforced systems before and after transposition have the same stability, the robust controller for the singular augmented error system can be obtained by the transposition system

Summary

Introduction

Since the singular system model [1] is proposed by Rosenbrock in the early 1970s, the singular system has been widely studied, and many results are obtained [2, 3]. Due to the modeling error, the measurement error, the linear approximation, and the change of working environment, the uncertainty of the system is objective They are presented as uncertain model parameters, system perturbation, measurement noise, external interference, etc. Because of the existence of the singular matrix, a proper Lyapunov function cannot be found by the current method to design the robust preview controller. Based on the method of [17], a Lyapunov function for the transposition system of the closed-loop system for the singular augmented error system is designed. Since the two unforced systems before and after transposition have the same stability, the robust controller for the singular augmented error system can be obtained by the transposition system. P > 0(P < 0) denotes the notion that matrix P is a positive definite (negative definite) matrix; I denotes the unit matrix; A ∈ Rm×n denotes a m × n matrix; the symbol ∗ denotes the symmetric terms in a symmetric matrix

Problem Statement

Construction of the Augmented Error System

Design of the Robust Preview Controller

Numerical Simulation

Conclusion