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This paper is concerned with a class of discrete-time stochastic systems with periodic coefficients and multiplicative noise. By use of an invariant-subspace approach, a simplified criterion is derived for detectability of the concerned systems. This spectral criterion can be verified by only examining the spectra of monodromy operator associated with real positive semi-definite matrices. Based on...
Serving as a great supplement for stochastic stability and stabilization, new notions called essential instability and essential destabilization are introduced. In this way, according to the spectral distribution of an uncontrolled linear time-invariant stochastic system in the complex plane, we distinguish three kinds of stabilities: asymptotical mean square stability, critical stability and essential...
In this note, we consider the finite horizon mixed H2/H∞ control problem for discrete-time stochastic linear systems subject to Markov jump parameters and multiplicative noise. Firstly, we derive a stochastic bounded real lemma (SBRL), which is used to establish a necessary and sufficient condition for the existence of the mixed H2/H∞ control via the solvability of four coupled difference matrix-valued...
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...
A stochastic singular linear quadratic (LQ) problem is considered under the condition that the state of the dynamics is partially observable. This paper gives the Kalman-Bucy filtering of the state by means of the Girsanov transformation, upon which the suboptimal linear feedback control of the LQ problem is determined. Furthermore, it is shown that the well-posedness of the LQ problem is equivalent...
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