GUARANTEED-COST STABILIZATION OF NONLINEAR STOCHASTIC-SYSTEMS

The control of uncertain non-linear discrete-time systems having stoch astic cone-bounded non-linearities is considered. First, a quadratic p erformance bound and a guaranteed-cost optimal state feedback controll er are derived. Then, an auxiliary system is introduced. It is shown t hat the quadratic optimal control for this auxiliary system is the sam e as the guaranteed-cost control for the original system, and, therefo re, the existence of the infinite-horizon guaranteed-cost controller c an be based on the stabilizability and observability properties of the auxiliary system. Finally, the stochastic boundedness of the controll ed uncertain system is proved based on the properties of the auxiliary system. (C) 1998 John Wiley & Sons, Ltd.