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Switched Systems

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Abstract

As the simplest hybrid system a switched system has many industrial backgrounds and engineering applications. Theoretically, it is also challenging: Switching adds complexity, and at the same time provides more freedom for control design. This chapter considers switched affine (control) systems. Section 15.1 investigates the problem of common quadratic Lyapunov function. It provides a tool for stability analysis and stabilization of switched linear systems. Section 15.2 gives a necessary and sufficient condition for quadratic stabilization of planar switched linear systems. Controllability of switched linear and bilinear control systems are studied in Sections 15.3 and 15.4 respectively. As an application, Section 15.5 considers the consensus of multi-agent systems.

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Author information

Authors and Affiliations

  1. Academy of Mathematics & Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Daizhan Cheng

  2. Optimization and Systems Theory, Royal Institute of Technology, 100 44, Stockholm, Sweden

    Xiaoming Hu

  3. Department of Engineering and Applied Sciences, Sophia University, Kiocho 7-1, Chiyoda-ku, Tokyo, 102-8554, Japan

    Tielong Shen

Authors
  1. Daizhan Cheng
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  2. Xiaoming Hu
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  3. Tielong Shen
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© 2010 Science Press Beijing and Springer-Verlag Berlin Heidelberg

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Cheng, D., Hu, X., Shen, T. (2010). Switched Systems. In: Analysis and Design of Nonlinear Control Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11550-9_15

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