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Hybrid Control of ADT Switched Linear Systems subject to Actuator Saturation

Fen Wu, Chengzhi Yuan

Abstract

This paper develops a hybrid output-feedback control framework for average dwell-time (ADT) switched linear systems subject to actuator saturation. The considered subsystems may be exponentially unstable, and the saturation nonlinearity is explicitly handled through a deadzone-based representation. The proposed hybrid controller combines mode-dependent full-order dynamic output-feedback controllers with a supervisory reset mechanism that updates controller states at switching instants. By incorporating the reset rule directly into the synthesis conditions, switching boundary constraints and performance requirements are addressed in a unified convex formulation. Sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to guarantee exponential stability under ADT switching and a prescribed weighted ${\cal L}_2$-gain disturbance attenuation level for energy-bounded disturbances. An explicit controller construction algorithm is provided based on feasible LMI solutions. Simulation results demonstrate the effectiveness and computational tractability of the proposed approach and highlight its advantages over existing output-feedback saturation control methods.

Hybrid Control of ADT Switched Linear Systems subject to Actuator Saturation

Abstract

This paper develops a hybrid output-feedback control framework for average dwell-time (ADT) switched linear systems subject to actuator saturation. The considered subsystems may be exponentially unstable, and the saturation nonlinearity is explicitly handled through a deadzone-based representation. The proposed hybrid controller combines mode-dependent full-order dynamic output-feedback controllers with a supervisory reset mechanism that updates controller states at switching instants. By incorporating the reset rule directly into the synthesis conditions, switching boundary constraints and performance requirements are addressed in a unified convex formulation. Sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to guarantee exponential stability under ADT switching and a prescribed weighted -gain disturbance attenuation level for energy-bounded disturbances. An explicit controller construction algorithm is provided based on feasible LMI solutions. Simulation results demonstrate the effectiveness and computational tractability of the proposed approach and highlight its advantages over existing output-feedback saturation control methods.
Paper Structure (7 sections, 3 theorems, 33 equations, 3 figures, 1 table)

This paper contains 7 sections, 3 theorems, 33 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Hybrid Control Synthesis
  4. Problem Statement
  5. Hybrid Control synthesis condition
  6. Illustrating Example
  7. Conclusions

Key Result

Lemma 1

Consider the switched nonlinear system Suppose there exist Lyapunov-like functions $V_i$, positive constants $a_i, b_i$, and scalars $\lambda_0 > 0$ and $\mu > 1$ such that, for all $x\in\mathbb{R}^n$ and all $i,j \in \mathbf{I}[1,N]$, Then system (NonPlant) is globally exponentially stable for every switching signal with average dwell time $\tau_a \geq \frac{\ln(\mu)}{\lambda_0}$. Note that the

Figures (3)

  • Figure 1: The proposed hybrid control scheme for saturated ADT switched systems.
  • Figure 2: Switching signal for the switched plant (\ref{['Sim.plant']}).
  • Figure 3: Simulation results

Theorems & Definitions (4)

  • Lemma 1: LibM.CSM99
  • Lemma 2: HuTZ2006
  • Theorem 1
  • Remark 1