Approximating Lyapunov exponents of switching systems

Abstract: In this talk I will discuss a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems. The proposed method allows to decide the uniform stability of a switching system and to compute the associated Lyapunov exponent with an arbitrary precision. The method relies on the discretization of the system and provides - for any given discretization stepsize - a lower and an upper bound for the Lyapunov exponent. Then I will briefly discuss asymptotic stability of continuous-time systems with mode-dependent guaranteed dwell time. These systems are reformulated as special cases of a general class of mixed (discrete-continuous) linear switching systems on graphs, in which some modes correspond to discrete actions and some others correspond to continuous-time evolutions.I will give a few examples to illustrate the methodology.

Mainly inspired by joint works with Vladimir Yu. Protasov (U. L’Aquila and Moscow State U.) and Marino Zennaro (U. Trieste).

mathematical physicsclassical analysis and ODEsdynamical systemsnumerical analysisprobabilitysymplectic geometry

Audience: researchers in the topic

Third DinAmicI Day

Series comments: The Giornata DinAmica (DAI Day) of the DinAmicI, the Community of Italian Dynamicists, takes place every two years and includes, in addition to scientific seminars, the assembly of members.

One of the aims of the DinAmicI is to promote young researchers: at least half of the invited speakers are in the early stage of their careers.

This third edition of the Day is exceptionally held online due to the restrictions caused by Covid and, exceptionally, the talks will be distributed over two afternoons.