Global Output Feedback Stabilization of Nonlinear Systems with a Time-Varying Power and Unknown Output Function

Chao Guo,Kemei Zhang

doi:10.1155/2018/2906469

Abstract

This paper studies the problem of global output feedback stabilization for a class of nonlinear systems with a time-varying power and unknown output function. For nonlinear systems with a time-varying power and unknown continuous output function, by constructing a new nonlinear reduced-order observer together with adding a power integrator method, a new function to determine the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, it is shown that the equilibrium point of the closed-loop system can be guaranteed globally uniformly asymptotically stable by an output feedback controller.

Highlights

IntroductionSome interesting results have been achieved on output feedback design of nonlinear systems with known constant powers and unknown output function
Consider nonlinear systems with the unknown output function xi (t) = [xi+1 (t)]p(t) + φi (t, x1 (t), . . . , xi (t)), i = 1, . . . , n − 1, (1)xṅ (t) = [u (t)]p(t) + φn (t, x1 (t), . . . , xn (t)), y (t) = h (x1 (t)), where x = (x1, . . . , xn)⊤ ∈ Rn, u ∈ R, and y ∈ R are the unmeasurable state, control input, and output, respectively
For nonlinear systems with a time-varying power, [27, 28] achieved global state feedback stabilization based on interval homogeneous domination approach

Summary

Introduction

Some interesting results have been achieved on output feedback design of nonlinear systems with known constant powers and unknown output function. For the nonlinear systems (1) with p(t) = 1, when h(⋅) is a continuous differentiable function and its derivative with known upper and lower bounds, global output feedback stabilization and finite-time output feedback stabilization have been achieved in [17,18,19] and [20], respectively. For nonlinear systems with a time-varying power, [27, 28] achieved global state feedback stabilization based on interval homogeneous domination approach. An interesting problem is put forward: For more general nonlinear systems (1) with h(x1) being an unknown continuous function, can we design an output feedback controller?.

Mathematical Preliminaries

Output Feedback Controller Design and Stability Analysis

Stability and Convergence Analysis

Simulation Example

Conclusions