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Robust stability and stabilization of the family of jumping stochastic systems. (English) Zbl 0942.93043
The author investigates exponential stability in mean square of the trivial solution of a linear stochastic differential equation driven by white noise, whose coefficients are governed by a finite-state Markov process \(i_t\) and which is controlled by a nonlinear feedback \(u(t)\).
Sufficient conditions are derived which (for given and arbitrary intensities of the white noise) yield the stability property in question, whatever the jump intensity \(q_{ij}\) of the Markovian background noise \(i_t\) may be (robustness).
Method: The problem is reduced to the algebraic problem of finding a positive definite matrix \(H\) which satisfies a system of nonlinear matrix equations labeled by the states \(i\) of the Markovian background noise.

93E15 Stochastic stability in control theory
93D15 Stabilization of systems by feedback
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
Full Text: DOI
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