Structural properties of linear stochastic systems
In this chapter we present the stochastic version of some basic concepts in control theory, namely stabilizability, detectability, and observability. All these concepts are defined both in Lyapunov operator terms and in stochastic system terms. The definitions given in this chapter extend the corresponding definitions from the deterministic time-varying systems. Some examples show that stochastic observability does not always imply stochastic detectability and stochastic controllability does not necessarily imply stochastic stabilizability. As in the deterministic case the concepts of stochastic detectability and observability are used in some criteria of exponential stability in the mean square.
KeywordsExponential Stability Stable Evolution Converse Implication Stochastic Matrix Stochastic Stabilizability
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