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Robust $$H_\infty$$ control of uncertain Markovian jump systems with time-delay. (English) Zbl 0983.93075
The authors consider a class of stochastic, uncertain linear state-delay dynamic systems. The time-varying uncertainties are modelled by sums of Markovian jump processes and real-valued functions representing time-varying parametric uncertainties. To obtain sufficient conditions on the existence of a robust stochastic stabilizing and $$\gamma$$-suboptimal $$H_\infty$$ state feedback controller, the authors apply the Lyapunov functional approach. In the construction of a robust stochastically stabilizing $$H_\infty$$ state feedback controller, the numerical solution of a set of coupled linear matrix inequalities is used.

##### MSC:
 93E20 Optimal stochastic control 93B36 $$H^\infty$$-control 15A39 Linear inequalities of matrices 93E15 Stochastic stability in control theory 93D21 Adaptive or robust stabilization 93C23 Control/observation systems governed by functional-differential equations
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