State Feedback Control of State-Delayed LPV Systems using Dynamic IQCs

TL;DR

This paper introduces a novel control framework for LPV systems with time-varying delays, combining parameter-dependent Lyapunov functions and dynamic IQCs to achieve stability and performance guarantees.

Contribution

It presents a new delay-dependent state-feedback control method using dynamic IQCs and parameter-dependent LMIs, offering improved flexibility and reduced conservatism over traditional approaches.

Findings

Ensures closed-loop stability with delay-varying LPV systems.

Provides convex synthesis conditions via LMIs for controller design.

Achieves enhanced control performance with systematic delay handling.

Abstract

This paper develops a new control framework for linear parameter-varying (LPV) systems with time-varying state delays by integrating parameter-dependent Lyapunov functions with integral quadratic constraints (IQCs). A novel delay-dependent state-feedback controller structure is proposed, consisting of a linear state-feedback law augmented with an additional term that captures the delay-dependent dynamics of the plant. Closed-loop stability and $\mathcal{L}_2$-gain performance are analyzed using dynamic IQCs and parameter-dependent quadratic Lyapunov functions, leading to convex synthesis conditions that guarantee performance in terms of parameter-dependent linear matrix inequalities (LMIs). Unlike traditional delay control approaches, the proposed IQC-based framework provides a flexible and systematic methodology for handling delay effects, enabling enhanced control capability, reduced conservatism, and improved closed-loop performance.