Robust H_infinity Filter Design for Lipschitz Nonlinear Systems via Multiobjective Optimization

TL;DR

This paper introduces a novel H_infinity observer design for Lipschitz nonlinear systems using LMI optimization, ensuring exponential convergence, robustness to disturbances, and maximization of the Lipschitz constant.

Contribution

It presents a new LMI-based method for designing robust H_infinity filters that simultaneously optimize the Lipschitz constant and disturbance attenuation level.

Findings

Guaranteed exponential decay rate of the observer

Maximized Lipschitz constant for robustness

Explicit bounds on tolerable nonlinear uncertainty

Abstract

In this paper, a new method of H_infinity observer design for Lipschitz nonlinear systems is proposed in the form of an LMI optimization problem. The proposed observer has guaranteed decay rate (exponential convergence) and is robust against unknown exogenous disturbance. In addition, thanks to the linearity of the proposed LMIs in the admissible Lipschitz constant, it can be maximized via LMI optimization. This adds an extra important feature to the observer, robustness against nonlinear uncertainty. Explicit bound on the tolerable nonlinear uncertainty is derived. The new LMI formulation also allows optimizations over the disturbance attenuation level (H_infinity cost). Then, the admissible Lipschitz constant and the disturbance attenuation level of the H_infinity filter are simultaneously optimized through LMI multiobjective optimization.