A common Lyapunov function for a differential inclusion with matrices having small commutators

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Abstract

Let A1 and A2 be asymptotically stable matrices. We consider switched continuous time linear systems described by the differential inclusion ẋ(t)={y(t):y(t)=Ax(t),A∈{A1,A2}}. The paper demonstrates that a common quadratic Lyapunov function exists for such systems, provided the commutator [A1,A2]=A1A2−A2A1 has a sufficiently small norm. Our results generalize the ones of Narendra and Balakrishnan (1994).

Original languageEnglish
JournalIFAC Journal of Systems and Control
Volume10
DOIs
StatePublished - 30 Dec 2019

Keywords

  • Common Lyapunov function
  • Continuous-time switched systems
  • Differential inclusion
  • Stability

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Artificial Intelligence
  • Computer Science Applications
  • Computer Networks and Communications
  • Management Science and Operations Research
  • Modeling and Simulation

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