Stability of linear autonomous systems under regular switching sequences

Yu Wang, Nima Roohi, Geir E. Dullerud, Mahesh Viswanathan

Research output: Contribution to journalConference article

Abstract

In this work, we discuss the stability of a discrete-time linear autonomous system under regular switching sequences, whose switching sequences are generated by a Muller automaton. The asymptotic stability of this system, referred to as regular asymptotic stability, generalizes two well-known definitions of stability of autonomous discrete-time linear switched systems, namely absolute asymptotic stability (AAS) and shuffle asymptotic stability (SAS). We also extend these stability definitions to robust versions. We prove that absolute asymptotic stability, robust absolute asymptotic stability and robust shuffle asymptotic stability are equivalent to exponential stability. In addition, by using the Kronecker product, we prove that a robust regular asymptotic stability problem is equivalent to the conjunction of several robust absolute asymptotic stability problems.

Original languageEnglish (US)
Article number7040240
Pages (from-to)5445-5450
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume2015-February
Issue numberFebruary
DOIs
StatePublished - Jan 1 2014
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: Dec 15 2014Dec 17 2014

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Autonomous Systems
Asymptotic stability
Asymptotic Stability
Linear Systems
Absolute Stability
Shuffle
Discrete-time
Switched Linear Systems
Kronecker Product
Exponential Stability
Automata
Generalise

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Stability of linear autonomous systems under regular switching sequences. / Wang, Yu; Roohi, Nima; Dullerud, Geir E.; Viswanathan, Mahesh.

In: Proceedings of the IEEE Conference on Decision and Control, Vol. 2015-February, No. February, 7040240, 01.01.2014, p. 5445-5450.

Research output: Contribution to journalConference article

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