Dissipativity-based static output feedback design for discrete-time LTI systems with time-varying input delays

TL;DR

This paper introduces new convex conditions based on dissipativity theory for designing static output feedback controllers for discrete-time systems with time-varying input delays, reducing conservatism compared to existing methods.

Contribution

It presents delay-dependent dissipativity-based convex conditions for static output feedback design using Lyapunov-Krasovskii functionals and Finsler's Lemma, with lower conservatism.

Findings

Conditions are expressed as linear matrix inequalities.

Designed controllers stabilize open-loop unstable systems.

Static state feedback gains are easily derived as a special case.

Abstract

This note is concerned with the presentation of new delay-dependent dissipativity-based convex conditions (expressed in the form of linear matrix inequalities) for the design of static output feedback (SOF) stabilizing gains for open-loop unstable discrete-time systems with input time-varying delays. A modified definition of QSR-dissipativity combined with the use of Lyapunov-Krasovskii functionals as storage functions and the application of Finsler's Lemma lead to the gathering of non-interactive design conditions. We show that, differently from most works dealing with controller design for time-delayed systems, the developed conditions present very small conservatism compared to stability analysis conditions derived with the same strategy. Due to being a particular case of SOF with an identity output matrix, static state feedback (SSF) gains can also trivially be computed from the conditions.