Robust discrete-time control for uncertain time-delay systems with nonlinearities under Hölder continuity

This paper is concerned with the robust discrete-time control for uncertain time-delay systems with nonlinearities and external noises. The parameter uncertainties enter into all the system matrices. The time-varying delay is unknown with given lower and upper bounds. The stochastic nonlinearities are described by satisfying a class of α Hölder condition. The problem addressed is the analysis and design of a stable controller such that, for all the parameter uncertainties, time-delay, stochastic nonlinearities and external noises, the resulting closed-loop system is exponentially stabile. The controller gain can be got by linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness and verify the proposed theoretical results.