Dwell-time control sets and applications to the stability analysis of linear switched systems

Francesco Boarotto (1, 2) , Mario Sigalotti (3, 4)

1 Dipartimento di Matematica "Tullio Levi-Civita"
2 Unipd - Università degli Studi di Padova = University of Padua
3 CaGE - Control And GEometry
4 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

We propose an extension of the theory of control sets to the case of inputs satisfying a dwell-time constraint. Although the class of such inputs is not closed under concatenation, we propose a suitably modified definition of control sets that allows to recover some important properties known in the concatenable case. In particular we apply the control set construction to dwell-time linear switched systems, characterizing their maximal Lyapunov exponent looking only at trajectories whose angular component is periodic. We also use such a construction to characterize supports of invariant measures for random switched systems with dwell-time constraints.

Mots clés: Linear switched systems; Control sets; Lyapunov exponents; Invariant measure

Domaines: Optimisation et contrôle [math.OC]

Francesco Boarotto, Mario Sigalotti. Dwell-time control sets and applications to the stability analysis of linear switched systems. Journal of Differential Equations, 2020, 268, pp.1345-1378. ⟨10.1016/j.jde.2019.08.049⟩. ⟨hal-02012606⟩