Abstract

Abstract: In this paper, the design problem of the state observer with the state feedback is investigated for the ‎stabilization of the discrete-time piecewise linear systems in the presence of uncertainty. In this paper, two uncertain ‎discrete-time systems are used which one of them has the external disturbance and the other does not. We used linear ‎matrix inequalities approach, piecewise quadratic Lyapunov functions and Finsler’s lemma for design of the state ‎observer. In addition to the above mentioned methods, we used ‎ control to design the state observer for the ‎uncertain system with external disturbance. The ‎ ‎ control causes the attenuation of the disturbance effect and ‎presents 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. Simulink results show the high performance of the ‎proposed method in stabilization of the closed-loop system and achievement of the acceptable estimation of state ‎variables.‎