A refinement of Matrosov’s theorem for differential inclusions

• Andrew R. Teel ^[1] ; Dragan Nešić ^[2] ; T.-C. Lee ^[3] ; Ying Tanb ^[2]
  1. [1] University of California, Santa Barbara

     University of California, Santa Barbara

     Estados Unidos

     
  2. [2] University of Melbourne

     University of Melbourne

     Australia

     
  3. [3] Minghsin University of Science and Technology,Taiwan

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• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 68, 2016, págs. 378-383
• Idioma: inglés
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• Resumen

  • This note presents a refinement of Matrosov’s theorem for a class of differential inclusions whose set-valued map is defined as a closed convex hull of finitely many vector fields. This class of systems may arise in the analysis of switched nonlinear systems when stability with arbitrary switching between the given vector fields is considered. Assuming uniform global stability of a compact set, it is shown that uniform global attractivity of the set can be verified by tailoring Matrosov functions to individual vector fields. This refinement of Matrosov’s theorem is an extension of the existing Matrosov results which may be easier to apply to certain differential inclusions than existing results, as demonstrated by an example.