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

Fen Wu

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.

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

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 -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.
Paper Structure (6 sections, 3 theorems, 29 equations, 1 figure, 1 table)

This paper contains 6 sections, 3 theorems, 29 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Formulation
  4. Delayed-Dependent Control Synthesis
  5. Numerical Example
  6. Concluding Remarks

Key Result

Lemma 1

Let $\Pi = \Pi^{\thicksim} \in \mathbf{RL}_\infty^{(m_1+m_2) \times (m_1+m_2)}$ be partitioned as where $\Pi_{11} \in \mathbf{RL}_\infty^{m_1 \times m_1}$ and $\Pi_{22} \in \mathbf{RL}_\infty^{m_2 \times m_2}$. If $\Pi_{11}(j \omega) > 0$ and $\Pi_{22}(j \omega) < 0$ for all $\omega \in \mathbf{R} \cup \{\infty\}$, then $\Pi$ admits a $J_{m_1,m_2}$-spectral factorization $(\Psi,W)$, also constit

Figures (1)

  • Figure 1: Simulation results.

Theorems & Definitions (6)

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