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Constrained Switching

  • Zhendong Sun
  • Shuzhi Sam Ge
Part of the Communications and Control Engineering book series (CCE)

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.

Keywords

Dwell Time Lyapunov Function Global Asymptotic Stability Switching Signal Switching Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.College Automation Science & Engineering, Center for Control and OptimizationSouth China University of TechnologyGuangzhouPeople’s Republic of China
  2. 2.Department of Electrical and Computer EngineeringThe National University of SingaporeSingaporeSingapore
  3. 3.Robotics Institue and Institute of Intelligent Systems and Information TechnologyUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China

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