Finite-time stability for discrete-time system with time-varying delay and nonlinear perturbations

- The problem of finite-time stability for discrete-time delayed system is studied.
- Discrete Wirtinger-based inequality and reciprocally convex approach are used in this paper.
- New criteria are established in terms of LMIs.
- Three numerical examples are given to show less conservatism of our obtained results.

In this paper, the problem of finite-time stability for discrete-time system with time-varying delay and nonlinear perturbations is investigated. By constructing a novel Lyapunov-Krasovskii functional and employing a new summation inequality named discrete Wirtinger-based inequality, reciprocally convex approach and zero equality, the improved finite-time stability criteria are derived to guarantee that the state of the system with time-varying delay does not exceed a given threshold when fixed time interval. Furthermore, the obtained conditions are formulated in forms of linear matrix inequalities which can be solved by using some standard numerical packages. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed method.