Global input-to-state stability and stabilization of discrete-time piece-wise affine systems

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This paper presents sufficient conditions for global Input-to-State (practical) Stability (ISpS) and stabilization of discrete-time, possibly discontinuous, Piece-Wise Affine (PWA) systems. Piece-wise quadratic candidate ISpS (ISS) Lyapunov functions are employed for both analysis and synthesis purposes. This enables us to obtain sufficient conditions based on linear matrix inequalities, which can be solved efficiently. One of the advantages of using the ISpS framework is that the additive disturbance inputs are explicitly taken into account in the analysis and synthesis procedures, and the results apply to PWA systems in their full generality, i.e. non-zero affine terms are allowed in the regions in the partition whose closure contains the origin. Copyright © 2006 IFAC.
Original languageEnglish
Pages (from-to)296-301
Number of pages6
JournalIFAC Proceedings Volumes
Issue number5
Publication statusPublished - 1 Dec 2006
Event2nd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS 2006 - Alghero, Italy
Duration: 7 Jun 20069 Jun 2006
Conference number: 2


  • Hybrid systems
  • Piece-wise affine systems
  • Robust stability
  • Stabilization methods


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