Stability and Stabilization of Delayed Discrete-Time System via a New Delay-Cubed-Dependent L–K Functional

The incorporation of matrix polynomial terms in the Lyapunov–Krasovskii (L–K) functional presents new challenges for the delayed discrete-time systems. This article proposes a novel delay-cubed-dependent L–K functional to alleviate the conservatism of the stability criteria for the discrete-time systems with time-varying delay. A novel matrix convex method is proposed to cope with the nonaffine terms introduced by the delay-cubed-dependent functional. Furthermore, a generalized matrix convex method is developed to address the L–K functional with varying orders of delay. Then, the executable stability and stabilization constraints with less conservatism are derived-based the proposed delay-cubed-dependent L–K functional and the matrix convex method. Finally, three case studies are given to elucidate the efficacy of the obtained stability and stabilization method.