A novel method to compute Lyapunov exponents of switched linear systems
Vortrag von Prof. Dr. Nicola Guglielmi
Sprecher eingeladen von: Prof. Dr. Stefan Sauter
Datum: 14.11.13 Zeit: 16.00 - 17.00 Raum: Y27H25
We consider switched linear systems of odes and propose a new method for the approximation of the upper Lyapunov exponent and - only for cooperative systems - the lower Lyapunov exponent. The method is based on the iterative construction of invariant polytopes for a sequence of discretized systems obtained by forcing the switching instants to be multiple of a given psitive number. These polytopes are then used to generate a piecewise-linear joint Lyapunov function, which gives tight upper and lower bounds for the Lyapunov exponents. As a byproduct we detect whether the considered system is stabilizable or uniformly stable. This is a joint work with L. Laglia (L'Aquila) and V. Protasov (Moscow).