Stability of discrete-time conewise linear inclusions and switched linear systems

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ACC2010_CLI.pdf (198.93 KB)

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https://ieeexplore.ieee.org/document/5530494

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https://doi.org/10.1109/ACC.2010.5530494
 http://hdl.handle.net/11603/35760

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UMBC Faculty Collection
UMBC Mathematics and Statistics Department

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Author/Creator ORCID

https://orcid.org/0000-0003-2172-4182

Date

2010-07-29

Type of Work

conference papers and proceedings
preprints
Text

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Program

Citation of Original Publication

Shen, Jinglai, and Jianghai Hu. “Stability of Discrete-Time Conewise Linear Inclusions and Switched Linear Systems.” In Proceedings of the 2010 American Control Conference, 4034–39, 2010. https://doi.org/10.1109/ACC.2010.5530494.

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© 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Subjects

Asymptotic stability
Control systems
Large-scale systems
Linear systems
Lyapunov method
Robots
Stability analysis
Stability criteria
Switched systems
Utility programs

Abstract

This paper addresses the stability of discrete-time conewise linear inclusions (CLIs) and its connection with that of switched linear systems (SLSs). The CLIs form a class of switched linear systems subject to state dependent switchings. Strong and weak stability concepts of the CLIs are considered and the equivalence of asymptotic and exponential stability is established. To characterize stability of the CLIs, a Lyapunov framework is developed and a converse Lyapunov theorem is obtained. Furthermore, stability of general SLSs is studied and is shown to be closely related to that of the CLIs through a family of properly defined generating functions.