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

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.

💡 Research Summary

This paper presents a novel control synthesis framework for linear parameter‑varying (LPV) systems that are subject to time‑varying state delays. The authors combine parameter‑dependent Lyapunov functions with dynamic integral quadratic constraints (IQCs) to model the delay operator in the frequency domain while preserving convexity in the design problem. The core contribution is a delay‑dependent state‑feedback law of the form

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