Reference : Instability and Overshoots of Solutions For A Class of Homogeneous Hybrid Systems By Lya...
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Instability and Overshoots of Solutions For A Class of Homogeneous Hybrid Systems By Lyapunov-like Analysis
Forni, Fulvio[Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation]
Teel, Andrew[UC Santa Barbara, CA > Electrical and Computer Engineering (ECE) > > >]
49th IEEE Conference on Decision and Control (cdc 2010)
2390 - 2395
49th IEEE Conference on Decision and Control (CDC), 2010
[en] instability ; sum of squares ; homogeneous hybrid systems
[en] For a class of homogeneous hybrid systems we present a generalization to the hybrid systems framework of Chetaev's theorem and we propose a set of Lyapunov-like conditions for studying instability of the point x e = 0 and overshoots of solutions (namely when the norm of the solution vector x at some time instant exceeds the norm of the initial condition of x). Based on these results, we design a sum of squares algorithm that constructs a suitable Lyapunov-like function to fulfill such conditions.