IQC-Based Output-Feedback Control of LPV Systems with Time-Varying Input Delays

TL;DR

This paper develops a convex, delay-dependent output-feedback control method for LPV systems with time-varying input delays using IQC framework, improving performance and reducing conservatism.

Contribution

It introduces a novel synthesis approach combining parameter-dependent Lyapunov functions and dynamic IQC multipliers for LPV systems with delays, with an explicit controller reconstruction formula.

Findings

Significant performance improvements demonstrated in numerical examples.

Reduced conservatism compared to existing methods.

Efficient computational approach for delay-dependent control design.

Abstract

Input delays are a common source of performance degradation and instability in control systems. This paper addresses the $\mathcal{H}_\infty$ output-feedback control problem for LPV systems with time-varying input delays under the integral quadratic constraint (IQC) framework. By integrating parameter-dependent Lyapunov functions with dynamic IQC multipliers, we derive convex, delay-dependent synthesis conditions formulated as parameter-dependent LMIs, enabled by the proposed exact-memory controller structure. An explicit controller reconstruction formula is provided to recover the LPV controller from the LMI solution, avoiding the need to specify the functional form of the parameter-dependent controller gains. While the synthesis problem for memoryless control is inherently non-convex, the proposed approach demonstrates significant performance improvement, reduced conservatism, and computational efficiency for standard output-feedback design. Numerical examples illustrate the effectiveness and broad applicability of the method to LPV systems with time-varying input delays.