Static State and Output Feedback Synthesis for Time-Delay Systems

TL;DR

This paper develops a method for designing static feedback gains for linear systems with input delays, using Lyapunov-Krasovskii stability analysis and iterative LMI procedures to reduce conservatism.

Contribution

It introduces a novel LMI-based iterative approach for static state and output feedback synthesis in time-delay systems, improving over existing methods.

Findings

The proposed method reduces conservatism in feedback design.

An iterative LMI procedure effectively handles non-convexities.

Comparison shows small conservatism compared to previous approaches.

Abstract

In this paper, the design of a static feedback gain for a linear system subject to an input delay is studied. This synthesis is based on a stability analysis conducted using Lyapunov-Krasovskii theorem and Bessel-Legendre inequalities expressed in terms of LMIs. Some bilinear non-convex matrix inequalities are obtained to go from analysis to synthesis. They are then difficult to solve and an iterative LMI procedure is given which takes advantage of the elimination lemma. Naturally, slack variables are introduced and then, following an optimization process, values for them are proposed to reduce the conservatism. The two main corollaries discuss the static state and output feedback synthesis. Finally, a comparison is proposed and shows that this formulation introduces small conservatism.