Stabilization of nonlinear delay systems: Adaptive impulsive observer-based saturated control approach

Abstract

This paper concentrates on stabilization problem of nonlinear delay systems involved unknown parameters via adaptive impulsive observer-based saturated control (AIOSC). Different from the existing literature that only the system state reconstruction and parameter estimation problems are comprehensively and thoroughly studied, we simultaneously solve the stabilization problem of such system itself. In virtue of an improved set inclusion relationship related to the augmented vector, the saturated effects on both impulsive correction and continuous control are explored in the sense of unmeasurable states. The main challenge of this paper is that with the help of the modified convex combination method, the time-varying Lyapunov function-based method, and comparison principle, how to fully utilize the systematic information to construct an elastic constraint relationship among system structure, delay information, and impulsive time sequence, which makes system parameters adjust appropriately as needed. Moreover, the maximum estimation of attractive domain is obtained by a convex optimal problem. And two examples are presented to demonstrate the validity of results, where stabilization of Lorenz system involved unknown parameters is considered.