Entropy for incremental stability of nonlinear systems under disturbances

TL;DR

This paper introduces entropy concepts for analyzing incremental stability of nonlinear systems under disturbances, providing bounds and a robust state estimation method based on finite approximating sets.

Contribution

It develops new entropy measures for incremental stability, establishes conditions for finite approximating sets, and proposes a robust state estimation algorithm for disturbed systems.

Findings

Bounds for estimation entropies are derived.

Finite approximating sets can be constructed under certain system conditions.

A robust state estimation algorithm using quantized measurements is proposed.

Abstract

Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which induces the desired stability properties, called an approximating set. We provide conditions on the system which ensures that the approximating set is finite. Lower and upper bounds for the two estimation entropies are computed. The construction of the finite approximating sets induces a robust state estimation algorithm for systems under disturbances using quantized and time-samples measurements.