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Constrained Switching

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Book cover Stability Theory of Switched Dynamical Systems

Part of the book series: Communications and Control Engineering ((CCE))

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Abstract

Chapter 3 presents stability theory for switched dynamical systems under constrained switching. There are three types of constrained switching addressed in this chapter. The first type of constrained switching is the random switching with a preassigned jump distribution. When the subsystems are linear and the switching is governed by a Markov process, the switched linear system is known to be a jump linear system. We introduce various stability concepts and their criteria and establish the connections to the guaranteed stability criteria in Chapter 2. The second is the piecewise affine systems, where the state space is partitioned into a set of polyhedral cells each relating to a subsystem, and hence the switching is totally autonomous. The piecewise quadratic Lyapunov approach, the surface Lyapunov approach, and the transition graph approach are introduced. The pros and cons of the approaches are compared and discussed. The third type of constrained switching is the dwell-time switching, where the switching duration between any two consecutive switches admits a positive lower bound. We address both the stability analysis, where the dwell time is preassigned, and the stabilizing switching design, where the minimum or maximum dwell time is to be designed. The design captures the capability and limitation of the switching mechanism.

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Authors and Affiliations

  1. College Automation Science & Engineering, Center for Control and Optimization, South China University of Technology, Guangzhou, 510640, People’s Republic of China

    Zhendong Sun

  2. Department of Electrical and Computer Engineering, The National University of Singapore, Singapore, Singapore

    Shuzhi Sam Ge

  3. Robotics Institue and Institute of Intelligent Systems and Information Technology, University of Electronic Science and Technology of China, Chengdu, People’s Republic of China

    Shuzhi Sam Ge

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  1. Zhendong Sun
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  2. Shuzhi Sam Ge
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Correspondence to Zhendong Sun .

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© 2011 Springer-Verlag London Limited

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Sun, Z., Ge, S.S. (2011). Constrained Switching. In: Stability Theory of Switched Dynamical Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-256-8_3

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  • DOI: https://doi.org/10.1007/978-0-85729-256-8_3

  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-255-1

  • Online ISBN: 978-0-85729-256-8

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