Stability and structural properties of stochastic periodic systems: An operator-spectral approach

Abstract

This paper addresses the stability and structural properties of discrete-time linear stochastic periodic systems with multiplicative noise. First, according to the spectral placement of a monodromy operator, spectral criteria are presented for asymptotic mean square stability, weak stability, observability and detectability, respectively. Further, it is shown that under the condition of observability (detectability), the asymptotic mean square stability of concerned systems is equivalent to the existence of positive (semi-)definite solution of a generalized periodic Lyapunov equation.