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   Polytope Lyapunov Functions for Stable and for Stabilizable LSS  
   
نویسنده Guglielmi Nicola ,Laglia Linda ,Protasov Vladimir
منبع foundations of computational mathematics - 2017 - دوره : 17 - شماره : 2 - صفحه:567 -623
چکیده    We present a new approach for constructing polytope lyapunov functions for continuous-time linear switching systems (lss). this allows us to decide the stability of lss and to compute the lyapunov exponent with a good precision in relatively high dimensions. the same technique is also extended for stabilizability of positive systems by evaluating a polytope concave lyapunov function (“antinorm”) in the cone. the method is based on a suitable discretization of the underlying continuous system and provides both a lower and an upper bound for the lyapunov exponent. the absolute error in the lyapunov exponent computation is estimated from above and proved to be linear in the dwell time. the practical efficiency of the new method is demonstrated in several examples and in the list of numerical experiments with randomly generated matrices of dimensions up to 10 (for general linear systems) and up to 100 (for positive systems). the development of the method is based on several theoretical results proved in the paper: the existence of monotone invariant norms and antinorms for positively irreducible systems, the equivalence of all contractive norms for stable systems and the linear convergence theorem.
کلیدواژه Linear switching systems ,Lyapunov exponent ,Polytope ,Iterative method ,Cones ,Metzler matrices ,Joint spectral radius ,Lower spectral radius ,15A60 ,15-04 ,15A18 ,90C90
آدرس University of L’Aquila, Dipartimento di Ingegneria Scienze Informatiche e Matematica, Italy. Gran Sasso Science Institute (GSSI), Italy, University of L’Aquila, Dipartimento di Ingegneria Scienze Informatiche e Matematica, Italy, Moscow State University, Department of Mechanics and Mathematics, Russia
 
     
   
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