Dead-beat stabilizability of autonomous switched linear discrete-time systems

Mirko Fiacchini (1) , Gilles Millérioux (2)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 CRAN - Centre de Recherche en Automatique de Nancy

The paper deals with dead-beat stabilizability of autonomous switched linear discrete-time systems. More precisely, it is investigated with the problem of finding a condition on the sequences of switches which guarantee that the state of the system reaches the origin in finite steps. A literature overview highlights the fact that such a problem is an open problem in the general case. First, we give necessary and sufficient conditions under which such an autonomous switched linear discrete-time system is dead-beat stabilizable. Then, an algorithm is proposed for deciding when such a sequence exists and for providing the sequence. It is shown that the complexity of the test can be much lower than the exhaustive search.

Domaines: Automatique / Robotique

Mirko Fiacchini, Gilles Millérioux. Dead-beat stabilizability of autonomous switched linear discrete-time systems. 20th IFAC World Congress, IFAC WC 2017, Jul 2017, Toulouse, France. ⟨10.1016/j.ifacol.2017.08.734⟩. ⟨hal-01569247⟩