Input-to-State Stabilization of a Class of Uncertain Nonlinear Systems via Observer-Based Event-Triggered Impulsive Control

Xiangru Xing,Jin-E Zhang

doi:10.1155/2020/3951381

Abstract

This article concerns the problem of input-to-state stabilization for a group of uncertain nonlinear systems equipped with nonabsolutely available states and exogenous disturbances. To appropriately cope with these partially measurable state variables as well as dramatically minimize controller updating burden and communication costs, an event-triggered mechanism is skillfully devised and an observer-based impulsive controller with the combination of sample control is correspondingly presented. By resorting to the iterative method and Lyapunov technology, some sufficient criteria are established to guarantee the input-to-state stability of the newly uncertain controlled system under the employed controller, in which an innovative approximation condition as to the uncertain term is proposed and the linear matrix inequality technique is utilized for restraining sophisticated parameter uncertainties. Furthermore, the Zeno behavior in the proposed event-triggered strategy is excluded. The control gains and event-triggered mechanism parameters are conjointly designed by resolving some inequalities of linear matrix. Eventually, the availability and feasibility of the achieved theoretical works are elucidated by two simulation examples.

Highlights

Since it is originally put forward by [1, 2], input-to-state stabilization has caught widespread attention [3,4,5], attributing to its performance in characterizing dynamical systems reaction to exogenous disturbances with bounded magnitude. e property of input-to-state stabilization, crudely speaking, symbolizes that the system state will approach the origin neighborhood whose dimension is in direct proportion to the size of the system input regardless of the magnitude of the initial state
Input-to-state stability behavior can characterize robustness and stability on dynamic systems possessed disturbances, in which the corresponding stabilization problem has a great signality for the control issue of [5,6,7]
Input-to-state stability is incipiently introduced for continuous systems to evaluate dynamical behaviors, which is especially a fundamental conception for investigating robust dynamics on nonlinear systems influenced by noise, inputs, or interferences [8]

Summary

Introduction

Since it is originally put forward by [1, 2], input-to-state stabilization has caught widespread attention [3,4,5], attributing to its performance in characterizing dynamical systems reaction to exogenous disturbances with bounded magnitude. e property of input-to-state stabilization, crudely speaking, symbolizes that the system state will approach the origin neighborhood whose dimension is in direct proportion to the size of the system input regardless of the magnitude of the initial state. In the control engineering application, when it comes to the fact that the system states may not be fully available because of implementation costs or physical restrictions, it becomes crucial and inevitable to formulate the event-triggered impulsive control strategy according to practical observer measurements At this juncture, once the incomplete testability of states and the uncertainty of parameters are incorporated into the characterization of nonlinear systems, these uncertainties may give rise to a totally new rule with more uncertain antecedents and results. What is exhilarating is that there is no work on the observer-based event-triggered impulsive control strategy to achieve the input-to-state property of uncertain nonlinear systems. E abovementioned analysis motivates us to focus on issues of both input-to-state stability and event-triggered impulsive control scheme design on a type of uncertain nonlinear systems with incomplete measurable state variables and exogenous disturbances in this paper.

Preliminaries and Model Description

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Illustrative Examples