A Lyapunov-based small-gain theorem for interconnected switched systems
Yang, Guosong
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https://hdl.handle.net/2142/45522
Description
Title
A Lyapunov-based small-gain theorem for interconnected switched systems
Author(s)
Yang, Guosong
Issue Date
2013-08-22T16:43:04Z
Director of Research (if dissertation) or Advisor (if thesis)
Liberzon, Daniel M.
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Nonlinear system
interconnected system
switched system
small-gain theorem
Lyapunov function
Abstract
Stability of an interconnected system consisting of two switched systems is investigated in the scenario where in both switched systems there may exist some subsystems that are not input-to-state stable (non-ISS). We have shown that, providing the switching signals neither switch too frequently nor activate non-ISS subsystems for too long, a small-gain theorem can be used to conclude global asymptotic stability (GAS) of the interconnected system. For each switched system, with the constraints on the switching signal being modeled by an auxiliary timer, a correspondent hybrid system is defined to enable the construction of hybrid ISS Lyapunov functions. Apart from justifying the ISS property of their corresponding switched systems, these hybrid ISS Lyapunov functions are then combined to establish a Lyapunov-type small-gain condition which guarantees that the interconnected system is globally asymptotically stable.
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