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Stability and stabilization for positive systems with semi-Markov switching. (English) Zbl 1460.93102

Summary: In this article, the problems of mean stability analysis and control synthesis are studied for stochastic switching systems subject to positive constraint. Such a switching is governed by a semi-Markov process subject to a special non-exponential distribution. Considering a linear Lyapunov-Krasovskii function (LKF), necessary and sufficient conditions are proposed to realize mean stability for the open-loop system. Based on this, the solvability conditions for the desired stabilizing controller can be determined under a linear programming (LP) framework. Finally, the theoretical findings are illustrated by the virus mutation treatment model.

MSC:

93E15 Stochastic stability in control theory
93C28 Positive control/observation systems
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
60K15 Markov renewal processes, semi-Markov processes
90C05 Linear programming
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