Stability Analysis of Hybrid Automata with Set-Valued Vector Fields Using Sums of Squares

Izumi MASUBUCHI  Tokihisa TSUJI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A    No.11    pp.3185-3191
Publication Date: 2006/11/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.11.3185
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Concurrent/Hybrid Systems: Theory and Applications)
Category: Hybrid Dynamical Systems
hybrid automata,  robust stability,  L2-gain,  sums of squares,  LMIs,  

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Stability analysis is one of the most important problems in analysis of hybrid dynamical systems. In this paper, a computational method of Lyapunov functions is proposed for stability analysis of hybrid automata that have set-valued vector fields. For this purpose, a formulation of matrix-valued sums of squares is provided and applied to derive an LMI/LME problem whose solution yields a Lyapunov function.