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This paper considers quadratic stabilizability and H∞ feedback control for stochastic discrete‐time uncertain systems with state‐ and control‐dependent noise. Specifically, the uncertain parameters considered are norm‐bounded and external disturbance is an l2‐square summable stochastic process. Firstly, both quadratic stability and quadratic stabilization criteria are presented in the form of linear matrix inequalities (LMIs). Then we design the robust H∞ state and output feedback H∞ controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust H∞ controllable. Sufficient conditions for the existence of the desired robust H∞ controllers are obtained via LMIs. Finally, some examples are supplied to illustrate the effectiveness of our results.

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Summary The global stabilization problem for a class of stochastic time‐delay nonlinear systems with stochastic‐input‐to‐state‐stable–like conditions is investigated. Different from the existing results, the nonlinear growing conditions are more general, and the existences of the state and input time delays make the work more challenging in the control design and stability analysis. By introducing an appropriate gain‐scaling method and using a homogeneous domain control strategy, a delay‐independent controller is constructed to ensure that the equilibrium at the origin of the closed‐loop system is globally asymptotically stable in probability. Examples are given to show the validness of the proposed method.

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