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Regional passivity for switched nonlinear systems and its application.

Yaowei Sun1, Jun Zhao2

  • 1College of Information Science and Engineering, State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China; College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, 466001, China.

ISA Transactions
|November 15, 2018
PubMed
Summary

This study introduces regional passivity theory for switched systems using barrier storage functions. It establishes conditions for regional passivity and asymptotic stability, applicable even when subsystems are not individually passive or stabilizable.

Keywords:
Barrier storage functionsRecursive backsteppingRegional passivitySwitched nonlinear systems

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Area of Science:

  • Control Theory
  • Nonlinear Systems
  • Dynamical Systems

Background:

  • Switched systems present unique stability challenges due to their piecewise nature.
  • Existing passivity theories often require subsystems to satisfy stringent conditions, limiting their applicability.
  • Regional passivity offers a more flexible framework for analyzing switched systems within specific operating regions.

Purpose of the Study:

  • To develop a novel framework for regional passivity theory tailored for switched systems.
  • To establish sufficient conditions for guaranteeing regional passivity and asymptotic stability in switched systems.
  • To extend the application of regional passivity to feedback interconnections and state-constrained nonlinear switched systems.

Main Methods:

  • Utilizing multiple barrier storage functions to define subsystem "energy" within open regions.
  • Deriving conditions for regional passivity under a designed switching law, without assuming individual subsystem passivity.
  • Analyzing asymptotic stability based on strict regional passivity or regional passivity with asymptotic detectability.
  • Investigating the preservation of regional passivity under feedback interconnections.

Main Results:

  • A sufficient condition for regional passivity of switched systems is established.
  • Conditions for achieving asymptotic stability are identified, contingent on system behavior within the defined regions.
  • Regional passivity is demonstrated to be robust under feedback interconnections.
  • The theory is successfully applied to solve the stabilization problem for state-constrained strict-feedback switched nonlinear systems.

Conclusions:

  • The developed regional passivity theory provides a powerful tool for analyzing and controlling complex switched systems.
  • The framework accommodates systems where individual subsystems may not meet traditional passivity or stability criteria.
  • This approach offers a pathway to stabilizing systems with state constraints and without requiring individual subsystem stabilizability.