Stabilizability of Discrete-Time Controlled Switched Linear Systems

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The goal of this paper is to study the stabilizability of controlled discrete-time switched linear systems (CSLSs), where the discrete switching control input and the continuous control input coexist. For a given positive integer h, we propose a quantitative metric of stabilizability, called h-contraction rate (h-CR), and prove that it serves as an indicator of the stabilizability in the following sense: the h-CR is less than one for sufficiently large h if and only if the switched linear system is stabilizable. In addition, we develop computational tools to estimate upper and lower bounds of the h-CR. In particular, the upper bound estimation is expressed as a semidefinite programming problem. We derive its Lagrangian dual problem and prove that the dual problem with an additional rank constraint gives an exact characterization of the h-CR. An algorithm is developed to solve the dual problem with the rank constraint.
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Issue Date
2018-10
Language
English
Article Type
Article
Citation

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, v.63, no.10, pp.3516 - 3522

ISSN
0018-9286
DOI
10.1109/TAC.2018.2794399
URI
http://hdl.handle.net/10203/272661
Appears in Collection
EE-Journal Papers(저널논문)
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