Observer Designing for Discrete-Time Piecewise Linear Systems: Linear Matrix Inequalities Approach

In this paper, the state feedback and design problem of state observer are presented to stabilize the discrete-time piecewise linear systems. In this article, we have two discrete-time systems that one of them is the disturbed system and the other is the system without disturbance. The linear matrix inequalities approach, piecewise quadratic Lyapunov functions and the Finsler’s lemma are used to design the state observer. In addition to the above mentioned methods, H∞ control approach used to design the state observer for the system with external disturbance. The H∞ control approach undermines the disturbance signal and provides an appropriate estimation of the system states. In this paper, by using the Finsler’s lemma, a set of slack variables are introduced to reduce the design conservatism. The Simulation results show the high performance of the proposed method for stabilize the closed-loop system and achieve to the acceptable estimation of state variables.