Stability of linear autonomous systems under regular switching sequences
Wang, Yu
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https://hdl.handle.net/2142/50614
Description
Title
Stability of linear autonomous systems under regular switching sequences
Author(s)
Wang, Yu
Issue Date
2014-09-16
Director of Research (if dissertation) or Advisor (if thesis)
Dullerud, Geir E.
Department of Study
Mechanical Sci & Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Switched systems
Muller Automata
Robust stability
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. This system arises in various engineering problems such as
distributed communication and automotive engine control. 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.
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