Linear Matrix Inequality Design of Exponentially Stabilizing Observer-Based State Feedback Port-Hamiltonian Controllers

TL;DR

This paper presents a method for designing observer-based controllers for port-Hamiltonian systems using linear matrix inequalities, ensuring passivity and exponential stability in infinite-dimensional cases and asymptotic stability in finite-dimensional nonlinear cases.

Contribution

It introduces a novel LMI-based design framework for passivity-guaranteed observer-based controllers for port-Hamiltonian systems, applicable to both infinite and finite-dimensional models.

Findings

Exponential stabilization of infinite-dimensional PHS achieved.

Asymptotic stabilization of finite-dimensional nonlinear PHS demonstrated.

Controller design verified on Timoshenko beam and MEMS models.

Abstract

The design of an observer-based state feedback (OBSF) controller with guaranteed passivity properties for port-Hamiltonian systems (PHS) is addressed using linear matrix inequalities (LMIs). The observer gain is freely chosen and the LMIs conditions such that the state feedback is equivalent to control by interconnection with an input strictly passive (ISP) and/or an output strictly passive (OSP) and zero state detectable (ZSD) port-Hamiltonian controller are established. It is shown that the proposed controller exponentially stabilizes a class of infinite-dimensional PHS and asymptotically stabilizes a class of finite-dimensional non-linear PHS. A Timoshenko beam model and a microelectromechanical system are used to illustrate the proposed approach.