Finite-time stabilization and H∞ control of Port-controlled Hamiltonian systems with disturbances and saturation.

Baozeng Fu,Ping Li,Qingzhi Wang,Yanzheng Zhu

doi:10.1371/journal.pone.0255797

Abstract

The finite-time stabilization and finite-time H∞ control problems of Port-controlled Hamiltonian (PCH) systems with disturbances and input saturation (IS) are studied in this paper. First, by designing an appropriate output feedback, a strictly dissipative PCH system is obtained and finite-time stabilization result for nominal system is given. Second, with the help of the Hamilton function method and truncation inequality technique, a novel output feedback controller is developed to make the PCH system finite-time stable when IS occurs. Further, a finite-time H∞ controller is designed to attenuate disturbances for PCH systems with IS, and sufficient conditions are presented. Finally, a numerical example and a circuit example are given to reveal the feasibility of the obtained theoretical results.

Highlights

The Port-controlled Hamiltonian (PCH) system has been studied well [1,2,3,4] since it was put forward [5, 6]
Lots of results on stability analysis and control designs for PCH systems have been presented based on Hamilton function method [14,15,16,17,18]
By utilizing the idea of constructing strictly dissipative PCH systems, the positive definite damping matrix can be obtained in the proof, which is very helpful to analyze the finite-time stability of the closed-loop system

Summary

Introduction

The Port-controlled Hamiltonian (PCH) system has been studied well [1,2,3,4] since it was put forward [5, 6]. For a class of Hamiltonian descriptor systems, the finite-time stabilization problem as well as the H1 control problem is studied utilizing the Hamilton function method in [30]. The finite-time stabilization problem for the case with IS is studied by designing an output feedback controller using the truncation inequality technique and Hamilton function method. We call this novel approach Hamilton function-based analysis method, which includes two cases. By utilizing the idea of constructing strictly dissipative PCH systems, the positive definite damping matrix can be obtained in the proof, which is very helpful to analyze the finite-time stability of the closed-loop system. The positive semi-definite matrix R(z) is denoted by R(z) 0. |a| stands for the absolute value of real number a. kRk represents the Euclidean norm of R. rE(z) denotes @E@ðzzÞ

A PCH system subject to disturbances and IS is considered

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Conclusion