Nonlinear Dynamics

, Volume 76, Issue 2, pp 1069–1077 | Cite as

Switching stabilization and \({ H}_{\varvec{\infty }}\) performance of a class of discrete switched LPV system with unstable subsystems

  • Xu He
  • Jun Zhao
Original Paper


Stability and \(H_\infty \) performance are analyzed in this paper for a class of discrete switched linear parameter-varying (LPV) systems in which all subsystems’ state-space matrices are parametrically affine, and any subsystem is not stable for parameters varying in a convex set. A switching law is designed to stabilize and satisfy the \(H_\infty \) performance of the switched LPV system. By means of the multiple Lyapunov functions method, linear matrix inequality (LMI) conditions for the existence of parameter-dependent Lyapunov functions are proposed. An example shows the effectiveness of the proposed methods.


Discrete switched LPV systems Unstable subsystems  Multi-Lyapunov functions Stability analysis \(H_\infty \) performance 



This study was supported by the Chinese National Fundamental Research Program under Grant 2009CB320601, and the National Natural Science Foundation of China under Grants 61233002 and 61174073.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.State Key Laboratory of Synthetical Automation for Process IndustriesNortheastern UniversityShenyang People’s Republic of China
  2. 2.State Key Laboratory of Robotics, Shenyang Institute of AutomationChinese Academy of SciencesShenyang People’s Republic of China

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