IQC Based Analysis and Estimator Design for Discrete-Time Systems Affected by Impulsive Uncertainties

TL;DR

This paper introduces a modular quadratic performance analysis framework for discrete-time impulsive systems using integral quadratic constraints, enabling systematic analysis and estimator design amid uncertainties.

Contribution

It presents novel IQC-based performance tests and a lossless LMI characterization for non-impulsive estimator existence in impulsive systems.

Findings

New IQC-based analysis framework for impulsive systems

Seamless extension to heterogeneous uncertainties

Numerical examples demonstrating effectiveness

Abstract

We propose novel quadratic performance tests for linear discrete-time impulsive systems based on viewing these systems as feedback interconnections of some non-impulsive linear system with an impulsive operator. In order to systematically analyze such interconnections, we employ the framework of integral quadratic constraints and propose novel constraints of this kind for capturing the behavior of the involved impulsive operator. As a major benefit, the modularity of this framework permits seamless extensions to interconnections affected by heterogeneous uncertainties in a straightforward fashion. This contrasts with alternative approaches which are based on capturing the system's impulsive behavior by means of a clock. Building upon the developed analysis criteria, we characterize the existence of non-impulsive estimators for such impulsive interconnections in a lossless fashion and in terms of linear matrix inequalities. Finally, our approach is illustrated by means of several numerical examples.