An application of forward difference method in robust stability of discrete uncertainty system with delays

Abstract

Abstract This paper deals with the problems of robust stability for a class of uncertainty parameter systems with delays. By using a new Lyapunov–Krasovskii functional, quadratic inequality, and Schur complement technique, two conditions are developed to guarantee the robust stability of a class of discrete systems with uncertainty parameters in terms of the linear matrix inequality (LMI). By applying the forward difference method and via a quadratic cost function, the criteria of LMI are obtained by the input control u(k)=0 $u(k)=0$ and u(k)=Kx(k) $u(k)=Kx(k)$; meanwhile, the bounds of cost function are established. The feedback control gain is designed to ensure the robust stability of the closed-loop system. A numerical example and simulation figures are provided to illustrate the effectiveness and potential of the proposed techniques and results.

Keywords

• Robust stability
• Forward difference
• Uncertainty system
• Schur complement