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

Fen Wu

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.

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

Abstract

Input delays are a common source of performance degradation and instability in control systems. This paper addresses the 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.
Paper Structure (7 sections, 3 theorems, 34 equations, 1 figure, 1 table)

This paper contains 7 sections, 3 theorems, 34 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Output Feedback Control Synthesis
  4. Exact-Memory Control
  5. Memoryless Control
  6. Numerical Study
  7. Conclusions

Key Result

Theorem 1

Consider the input-delayed LPV plant (Plant). If there exist positive-definite matrix functions $R, S: \mathbf{R}_+ \rightarrow \mathbf{S}_+^{n_{aug}}$, positive-definite matrix functions $\hat{X}_k \in \mathbf{S}_+^{n_u}, k \in {\bf I}[1, N_{\lambda}]$, a rectangular matrix function $X \in \mathbf{ where ${\cal N}_R = {\rm Ker} , {\cal N}_S = {\rm Ker} $, and $\Lambda = {\rm diag} \left\{ X_1(\rh

Figures (1)

  • Figure 1: The feedback system with a delay loop.

Theorems & Definitions (5)

  • Definition 1: Sei.TAC14
  • Theorem 1
  • Theorem 2
  • Remark 1
  • Corollary 1