Memory Resilient Gain-scheduled State-Feedback Control of Uncertain LTI/LPV Systems with Time-Varying Delays

TL;DR

This paper develops a novel memory resilient gain-scheduled state-feedback control method for uncertain LTI/LPV systems with time-varying delays, unifying memoryless and exact-memory controllers, and uses LMIs for stability and performance optimization.

Contribution

It introduces a unified controller design framework that handles uncertainties in delay knowledge, combining memoryless and exact-memory strategies with LMI-based stability and performance analysis.

Findings

Controllers ensure stability under delay uncertainties.

LMI conditions enable delay uncertainty radius optimization.

Approach improves robustness and performance in uncertain delay systems.

Abstract

The stabilization of uncertain LTI/LPV time delay systems with time varying delays by state-feedback controllers is addressed. At the difference of other works in the literature, the proposed approach allows for the synthesis of resilient controllers with respect to uncertainties on the implemented delay. It is emphasized that such controllers unify memoryless and exact-memory controllers usually considered in the literature. The solutions to the stability and stabilization problems are expressed in terms of LMIs which allow to check the stability of the closed-loop system for a given bound on the knowledge error and even optimize the uncertainty radius under some performance constraints; in this paper, the $\mathcal{H}_\infty$ performance measure is considered. The interest of the approach is finally illustrated through several examples.