Systems with both constant and time-varying delays: a switched systems approach and application to observer-controller co-design

TL;DR

This paper introduces a novel switched systems approach using path-complete Lyapunov techniques and a new functional to analyze systems with constant and time-varying delays, enabling delay-dependent stability conditions and observer-controller design.

Contribution

It presents a new convex analysis method avoiding dwell time computation, applying to systems with mixed delays and facilitating observer-controller co-design.

Findings

Derived delay-dependent stability conditions for systems with mixed delays.

Developed LMIs for closed-loop stabilization with observer-based controllers.

Demonstrated effectiveness through a numerical example.

Abstract

In this paper, we study the application of switched systems stability criteria to derive delay-dependent conditions for systems affected by both a constant and a time-varying delay. The main novelty of our approach lies on the use of path-complete Lyapunov techniques along with the proposition of a new modified functional to obtain convex analysis conditions while avoiding the need of computing a dwell time for each mode in a switched system representation, as usual in the \textit{switched approach} for time-delay systems. Furthermore, we leverage the developed analysis to obtain LMIs for the closed-loop stabilization of systems with time-varying sensor delays by means of an observer-based compensator. A numerical example illustrates the proposed methods.