Quadratic stabilizability and H control of linear discrete-time stochastic uncertain systems

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 l(2)-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.