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

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.

Guaranteed cost control for exponential stability of a nonlinear system with mixed time-varying delays in states and controls

“…Recently, the basic theoretical and practical problem of exponential stability and control of a delayed nonlinear system has also been investigated by some researchers [15][16][17][18] because it is also an important index to obtain the convergence rates of prescribed time-delay systems. In [15], the problem of exponential stabilization of nonlinear dynamical systems with delayed perturbations was studied by constructing a quadratic Lyapunov functional.…”

Dynamic output feedback control based on virtual feedback control law for planar switched nonlinear systems with time-varying delays and multiple subsystems

“…Compared with the controller design for the SISO system, the control issues for the MIMO system are more difficult and challenging. For the MIMO nonlinear dynamic systems with time-delay and dead-zone inputs, the delay-dependent exponential stabilization criteria were proposed for a class of nonlinear systems with mixed time-varying delays in [15]. In [16], the MIMO underactuated nonlinear system was in the form of block-triangular structure, and the novel controller was designed based on the back-stepping method.…”