Static Output Feedback Stabilization of Linear Systems with Multiple Delays

TL;DR

This paper introduces a novel convex optimization-based method for stabilizing linear systems with multiple delays using Static Output Feedback, extending existing approaches to infinite-dimensional systems.

Contribution

It extends convex optimization techniques for SOF stabilization to time-delay systems via a new state-space representation and the use of the Projection Lemma for PI operators.

Findings

Significant reduction in conservatism compared to existing SOF methods

Extension of LMIs to infinite-dimensional systems for delay stabilization

Comparison shows improved performance over previous solutions

Abstract

This work proposes a new procedure for the stabilization of time-delay systems using Static Output Feedback (SOF) control. A previous convex optimization approach to SOF for Ordinary Differential Equations (ODEs) is extended to time-delay systems through the use of a proposed state-space representation. This approach is based on solving two convex optimization problems, which are extensions of Linear Matrix Inequalities (LMIs) to infinite-dimensional systems. The first problem is stabilization under state feedback control; the second problem takes advantage of the Projection Lemma, which is extended here from matrices to Partial Integral (PI) operators. Finally, the results are compared with other SOF solutions for systems with delay found in the literature, showing a significant reduction in conservatism.