Parameter Estimation-Based Observer for Linear Systems with Polynomial Overparametrization

TL;DR

This paper introduces a novel adaptive observer for overparametrized linear systems that does not require canonical form or gain identification, ensuring exponential convergence with weak excitation conditions.

Contribution

It develops a parameter estimation-based observer that handles overparametrization and unknown output matrices without canonical form constraints.

Findings

Ensures exponential convergence of state estimation error.

Applicable to systems with unknown output matrices.

Validated through simulation results.

Abstract

An adaptive state observer is proposed for a class of overparametrized uncertain linear time-invariant systems without restrictive requirement of their representation in the observer canonical form. It evolves the method of generalized parameters estimation-based observer design and, therefore, (i) does not require to identify Luenberger correction gain parameters, (ii) forms states using algebraic rather than differential equation. Additionally, the developed observer is applicable to systems with unknown output matrix and ensures exponential convergence of unmeasured state observation error under weak requirement of the regressor finite excitation. The effectiveness of the proposed solution is supported by simulation results.