Observer design for classes of nonlinear port-Hamiltonian systems

TL;DR

This paper develops a systematic observer design method for nonlinear port-Hamiltonian systems with state-dependent input matrices, using LPV embedding and LMI conditions to ensure exponential convergence.

Contribution

It introduces a novel LPV polytopic embedding framework with LMI-based synthesis for observer design in nonlinear port-Hamiltonian systems.

Findings

Gain-scheduled observers outperform constant-gain in decay rate.

Numerical results confirm effectiveness and reduced conservatism.

Method applicable to electromechanical systems like MEMS and actuators.

Abstract

This paper presents a systematic observer design methodology for a class of port-Hamiltonian (pH) systems with state-dependent input matrices. Such systems can model a wide range of electromechanical systems, including magnetic levitation systems, MEMS devices, and electro-active polymer actuators such as DEA actuators, HASEL actuators, etc. In these applications, state-dependent input matrices naturally arise when the system is modeled under quasi-static electrical assumptions. An LPV polytopic embedding framework, together with LMI-based synthesis conditions, is proposed. The nonlinear error dynamics are represented as a convex combination of linear vertex systems using an integral mean value representation, which enables systematic computation of the observer gains that ensures exponential convergence. Both constant-gain and gain-scheduled observers are derived. Numerical results demonstrate the effectiveness of the proposed observer, with the gain-scheduled design achieving a significant increase in the maximum certifiable decay rate compared with constant-gain approaches, thereby reducing conservatism.