Exact Detectability of Discrete-Time and Continuous-Time Linear Stochastic Systems: A Unified Approach

This article is devoted to the problem of detectability of a large class of linear stochastic systems with time varying coefficients simultaneously affected by state multiplicative white noise perturbations and Markovian switching. The main contribution of this article is to propose a Popov–Belevich–Hautus-type test, which is equivalent to the detectability of the considered stochastic systems in the sense that all unstable modes produce some nonzero output. The proposed setting unifies in some sense the discrete-time and continuous-time ones, dissimilarly to the vast majority of existing works that study discrete and continuous time separately.