State measurement error-to-state stability results based on approximate discrete-time models

TL;DR

This paper extends stability analysis for nonlinear systems with approximate discrete-time models by incorporating state-measurement errors and varying sampling rates, providing conditions for practical stability using Lyapunov functions.

Contribution

It introduces new ISS-based stability results considering measurement errors and variable sampling, filling gaps in existing stability theory for approximate models.

Findings

Bounded measurement errors can cause divergence in practical stability.

New Lyapunov-based conditions ensure semiglobal practical ISS.

Numerical examples demonstrate the impact of measurement errors on stability.

Abstract

Digital controller design for nonlinear systems may be complicated by the fact that an exact discrete-time plant model is not known. One existing approach employs approximate discrete-time models for stability analysis and control design, and ensures different types of closedloop stability properties based on the approximate model and on specific bounds on the mismatch between the exact and approximate models. Although existing conditions for practical stability exist, some of which consider the presence of process disturbances, input-to-state stability with respect to state-measurement errors and based on approximate discretetime models has not been addressed. In this paper, we thus extend existing results in two main directions: (a) we provide input-to-state stability (ISS)-related results where the input is the state measurement error and (b) our results allow for some specific varying-sampling-rate scenarios. We provide conditions to ensure semiglobal practical ISS, even under some specific forms of varying sampling rate. These conditions employ Lyapunov-like functions. We illustrate the application of our results on numerical examples, where we show that a bounded state-measurement error can cause a semiglobal practically stable system to diverge.