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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...
This paper addresses observability and detectability of discrete-time periodic systems with nonhomogeneous Markov jump parameter. Popov–Belevitch–Hautus (PBH)-type criteria are proposed for the concerned structural properties. It is shown that, different from stochastic systems with constant coefficients or homogeneous Markov chain, the spectral criteria of considered plants do not rely on a single...
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...
A new criterion is proposed for exact observability of linear stochastic systems. As applications of it, the effects of exact observability due to state/output feedback are investigated. In addition, under the conditions of stability and exact observability, we discuss the property of a set defined by the generalized Lyapunov equations. Finally, with the aid of spectrum technique, we introduce a new...
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