Observability and detectability of periodic markov jump systems with multiplicative noises

Based on a newly proposed monodromy operator, spectral criteria are developed for stability, observability and detectability of discrete-time Markov jump systems with periodically time-varying coefficients and transition probability matrix. Moreover, it is shown that the obtained structural criteria have important applications in the analysis about asymptotic mean square stability of periodic Markov jump systems and stabilizing solution of periodic difference Riccati equations.