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Finite-time and bumpless transfer control of asynchronously switched systems: An output feedback control approach

Mo-Ran Liu, Zhen Wu, Xian Du, Zhongyang Fei

TL;DR

This work tackles finite-time stabilization and bumpless transfer for asynchronously switched systems using dynamic output feedback plus a smoothing filter. By decoupling the closed-loop dynamics and formulating controller-gain design as solvable LMIs, it delivers explicit conditions for finite-time stability, finite-time boundedness, and $H_infty$ performance under disturbances, all within an average dwell time framework. The approach yields practical gain synthesis with controller updates that minimize control bumps and ensure state bounds over short time horizons, demonstrated on a boost converter example. The results advance transient-performance guarantees for switching systems where mode activation is asynchronous, and provide a foundation for extending to more uncertain or complex switching scenarios. Overall, the method offers a rigorous, implementable route to robust, bumpless, finite-time control in practical electro-mechanical systems.

Abstract

In this paper, the finite-time control and bumpless transfer control are investigated for switched systems under asynchronously switching. First, a class of dynamic output feedback controllers are designed to stabilize the switched system with measurable system outputs. Considering the improvement of transient performance, the bumpless transfer control and finite-time control are further studied in the controller design. To avoid the control bumps, a practical filter is introduced to make the control signal smoother and continuous. Furthermore, to derive a finite-time bounded system state over short-time intervals, the finite-time analysis is considered in managing the switching process with the average dwell time. New criteria are proposed to analyze the finite-time stability and finite-time boundedness for the closed-loop system and solvable conditions are newly proposed to optimize the controller gain. Finally, the superiorities of the proposed method are validated through an application to a boost converter.

Finite-time and bumpless transfer control of asynchronously switched systems: An output feedback control approach

TL;DR

This work tackles finite-time stabilization and bumpless transfer for asynchronously switched systems using dynamic output feedback plus a smoothing filter. By decoupling the closed-loop dynamics and formulating controller-gain design as solvable LMIs, it delivers explicit conditions for finite-time stability, finite-time boundedness, and performance under disturbances, all within an average dwell time framework. The approach yields practical gain synthesis with controller updates that minimize control bumps and ensure state bounds over short time horizons, demonstrated on a boost converter example. The results advance transient-performance guarantees for switching systems where mode activation is asynchronous, and provide a foundation for extending to more uncertain or complex switching scenarios. Overall, the method offers a rigorous, implementable route to robust, bumpless, finite-time control in practical electro-mechanical systems.

Abstract

In this paper, the finite-time control and bumpless transfer control are investigated for switched systems under asynchronously switching. First, a class of dynamic output feedback controllers are designed to stabilize the switched system with measurable system outputs. Considering the improvement of transient performance, the bumpless transfer control and finite-time control are further studied in the controller design. To avoid the control bumps, a practical filter is introduced to make the control signal smoother and continuous. Furthermore, to derive a finite-time bounded system state over short-time intervals, the finite-time analysis is considered in managing the switching process with the average dwell time. New criteria are proposed to analyze the finite-time stability and finite-time boundedness for the closed-loop system and solvable conditions are newly proposed to optimize the controller gain. Finally, the superiorities of the proposed method are validated through an application to a boost converter.
Paper Structure (9 sections, 6 theorems, 95 equations, 5 figures)

This paper contains 9 sections, 6 theorems, 95 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation and Preliminaries
  3. Finite-time stability and boundedness analysis
  4. Parameter optimization
  5. Illustrative Example
  6. Conclusions
  7. Proof of theorem \ref{['thm1']}
  8. Proof of theorem \ref{['thm2']}
  9. Proof of theorem \ref{['thm3']}

Key Result

Lemma 1

The following conditions involving real scalar $\varepsilon$ and real matrices $W$, $X$, $Y$, and $Z$ are equivalent. 1) There exist real scalar $\varepsilon$ and and real matrices $W$, $X$, $Y$, and $Z$ such that 2) There exist real matrices $W$, $X$ and $Y$ such that

Figures (5)

  • Figure 1: The boost converter circuit system.
  • Figure 2: Controller output and switching signals.
  • Figure 3: The state trajectories of system (\ref{['1']}).
  • Figure 4: Controller output with ${H}_\infty$ performance and switching signals.
  • Figure 5: The state trajectories of system (\ref{['1']}) with external disturbance.

Theorems & Definitions (18)

  • Definition 1: See Hespanha1999
  • Definition 2: See liu2014finite
  • Definition 3: See LIN20115982
  • Definition 4: See liu2014finite
  • Lemma 1: See Zhou2016non
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Theorem 1
  • ...and 8 more