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A unified design for state and output feedback \(H_\infty \) control of nonlinear stochastic Markovian jump systems with state and disturbance-dependent noise. (English) Zbl 1192.93029

Summary: For a class of continuous-time nonlinear stochastic Markovian jump systems with state- and disturbance-dependent noise, both the state and output feedback \(H_\infty \) control problems are studied. Based on the solvability of a set of coupled Hamilton-Jacobi inequalities (HJIs), we give a unified design for both state and dynamic output feedback \(H_\infty \) control via a common function \(u(\cdot ,r_t)\) (i.e., \(u(x,r_t)\) is a state feedback \(H_\infty \) control, while \(u(\hat x ,r_t)\) is the desired output feedback \(H_\infty \) control).

MSC:

93B36 \(H^\infty\)-control
93C10 Nonlinear systems in control theory
93E03 Stochastic systems in control theory (general)
60J75 Jump processes (MSC2010)
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