Robust nonlinear observer design based on impulsive dissipativity

TL;DR

This paper develops a nonlinear impulsive observer that guarantees exponential convergence and input-to-state stability using dissipativity theory, accommodating non-periodic measurements and uncertainties.

Contribution

It introduces a novel nonlinear dissipative impulsive observer with derived conditions for stability and convergence, integrating impulsive and dissipative systems theory.

Findings

Conditions for exponential convergence without measurement uncertainty.

Input-to-state stability conditions with measurement uncertainty.

Illustrative case example demonstrating theoretical results.

Abstract

The paper considers the design of a nonlinear dissipative impulsive observer based on non-periodic discrete-time measurements. Sufficient conditions are derived for (i) exponential convergence of the observer in absence of measurement uncertainty, and (ii) input-to-state stability (ISS) with respect to measurement uncertainty, by combining notions from impulsive and dissipative systems theory. The conditions mainly include constraints on the minimum and maximum time between measurements depending on system characteristics, the correction gain and the desired ISS gain. A representative case example is used to illustrate the theoretical assessments.