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

2021/07/02 by Lima, Thiago Alves, Madeira, Diego de S.
#FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2107.01138

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.

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