Observers for differential-algebraic systems with Lipschitz or monotone nonlinearities

TL;DR

This paper develops a unified observer design for nonlinear differential-algebraic systems with Lipschitz or monotone nonlinearities, extending classical methods and providing a systematic way to compute observer parameters.

Contribution

It introduces a generalized observer design framework that encompasses previous approaches and utilizes linear matrix inequalities for parameter computation.

Findings

Unified observer design for Lipschitz and monotone nonlinearities

Extension of Luenberger observer to differential-algebraic systems

Illustrative examples demonstrating effectiveness

Abstract

We study state estimation for nonlinear differential-algebraic systems, where the nonlinearity satisfies a Lipschitz condition or a generalized monotonicity condition or a combination of these. The presented observer design unifies earlier approaches and extends the standard Luenberger type observer design. The design parameters of the observer can be obtained from the solution of a linear matrix inequality restricted to a subspace determined by the Wong sequences. Some illustrative examples and a comparative discussion are given.