Design of Nonlinear State Observers for One-Sided Lipschitz Systems

TL;DR

This paper extends nonlinear state observer design to systems with one-sided Lipschitz functions, offering less conservative and more general solutions compared to traditional Lipschitz-based methods.

Contribution

It introduces a novel observer design framework for one-sided Lipschitz systems, expanding the class of systems that can be effectively estimated.

Findings

Proposes a new observer design method using nonlinear matrix inequalities.

Transforms nonlinear matrix inequalities into linear ones for computational efficiency.

Demonstrates improved estimation performance over traditional Lipschitz-based observers.

Abstract

Control and state estimation of nonlinear systems satisfying a Lipschitz continuity condition have been important topics in nonlinear system theory for over three decades, resulting in a substantial amount of literature. The main criticism behind this approach, however, has been the restrictive nature of the Lipschitz continuity condition and the conservativeness of the related results. This work deals with an extension to this problem by introducing a more general family of nonlinear functions, namely one-sided Lipschitz functions. The corresponding class of systems is a superset of its well-known Lipschitz counterpart and possesses inherent advantages with respect to conservativeness. In this paper, first the problem of state observer design for this class of systems is established, the challenges are discussed and some analysis-oriented tools are provided. Then, a solution to the observer design problem is proposed in terms of nonlinear matrix inequalities which in turn are converted into numerically efficiently solvable linear matrix inequalities.