Output Regulation of Linear Aperiodic Sampled-Data Systems

TL;DR

This paper addresses the output regulation challenge for linear systems with sporadically available measurements by designing a hybrid regulator that ensures stability and regulation despite measurement intermittency.

Contribution

It introduces a novel regulator with a reset-based intersample injection mechanism analyzed within a hybrid system framework, providing a tractable design via linear matrix inequalities.

Findings

Sufficient conditions for stability under intermittent measurements

A hybrid regulator design method based on LMIs

Validation through an illustrative example

Abstract

This paper deals with the output regulation problem of a linear time-invariant system in the presence of sporadically available measurement streams. A regulator with a continuous intersample injection term is proposed, where the intersample injection is provided by a linear dynamical system and the state of which is reset with the arrival of every new measurement updates. The resulting system is augmented with a timer triggering an instantaneous update of the new measurement and the overall system is then analyzed in a hybrid system framework. With the Lyapunov based stability analysis, we offer sufficient conditions to ensure the objectives of the output regulation problem are achieved under intermittency of the measurement streams. Then, from the solution to linear matrix inequalities, a numerically tractable regulator design procedure is presented. Finally, with the help of an illustrative example, the effectiveness of the theoretical results are validated.