Observer design for nonlinear triangular systems with unobservable linearization

TL;DR

This paper develops observer design methods for a broad class of nonlinear triangular systems with unobservable linearizations, providing conditions for Luenberger-type observers and a switching-based estimation approach.

Contribution

It introduces new observer design techniques for nonlinear systems with unobservable linearizations, including conditions for Luenberger observers and a switching sequence method.

Findings

Derived sufficient conditions for Luenberger observer existence

Proposed a switching sequence approach for general cases

Applicable to time-varying nonlinear triangular systems

Abstract

The paper deals with the observer design problem for a wide class of triangular time-varying nonlinear systems, with unobservable linearization. Sufficient conditions are derived for the existence of a Luenberger-type observer, when it is a priori known that the initial state of the system belongs to a given nonempty bounded subset of the state space. For the general case, the state estimation is exhibited by means of a switching sequence of time-varying dynamics