Exact detectability and exact observability of discrete-time linear stochastic systems with periodic coefficients

Vasile Dragan (1, 2) , Samir Aberkane (3)

1 IMAR - "Simion Stoilow" Institute of Mathematics
2 The Academy of the Romanian Scientists
3 CRAN - Centre de Recherche en Automatique de Nancy

This paper is devoted to the problem of detectability and observability of a class of time-varying stochastic systems. The main contribution of this note is to propose a PBH-type test which is equivalent to the detectability of the considered stochastic systems in the sense that all unstable modes produce some non-zero output. Then, we apply the obtained results in order to derive a criterion of exponential stability in mean square sense as well as existence conditions for the stabilizing solution of a class of discrete-time time-varying Riccati equations.

Mots clés: Discrete-time stochastic systems; Periodic coefficients; Exact detectability; Exact observability; PBH type criterion; Characteristic multipliers

Domaines: Optimisation et contrôle [math.OC]

Vasile Dragan, Samir Aberkane. Exact detectability and exact observability of discrete-time linear stochastic systems with periodic coefficients. Automatica, 2020, 112, pp.108660. ⟨10.1016/j.automatica.2019.108660⟩. ⟨hal-02940983⟩