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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.

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