Global asymptotic stabilisation for switched planar systems

Junfeng Zhang, Zhengzhi Han and Jun Huang

International Journal of Systems Science, 2015, vol. 46, issue 5, 908-918

Abstract: This paper studies the stabilisation problem of a class of switched planar systems. The present method is different from the existing one designing directly controllers for the underlying systems. The controllers are constructed through two steps. Firstly, by means of the backstepping approach, homogeneous controllers stabilising the nominal systems are obtained. Secondly, the controllers stabilising the planar subsystems are attained by modifying the obtained homogeneous controllers. The controllers depend on perturbations of the switched systems. Finally, by using the multiple Lyapunov functions approach, a sufficient condition of the stabilisation for switched planar systems is given. The conclusions are extended to multiple dimensional switched systems. An illustrative example verifies the validity of the design.

Date: 2015
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DOI: 10.1080/00207721.2013.801093

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