Novel delay-dependent exponential stabilization criteria of a nonlinear system with mixed time-varying delays via hybrid intermittent feedback control

Abstract

Abstract In this paper, we investigate the problem of exponential stabilization criteria for a nonlinear system with mixed time-varying delays, including discrete interval and distributed time-varying delays. The time-varying delays are not necessarily differentiable. The exponential stabilization criteria of the nonlinear system are proposed via hybrid intermittent feedback control. Based on the improved Lyapunov-Krasovskii functionals with Leibniz-Newton’s formula, Jensen’s inequality and the reciprocal convex combination technique, the novel delay-dependent sufficient condition is derived in terms of linear matrix inequalities (LMIs). The obtained LMIs can be efficiently solved by standard convex optimization algorithms. A numerical example is given to demonstrate the effectiveness of the obtained result. Moreover, the results in this article generalize and improve the corresponding results of the recent works.

Keywords

• exponential stabilization
• nonlinear system
• mixed time-varying delays
• hybrid intermittent feedback control