Stability analysis and guaranteed cost control for stochastic nonlinear quadratic systems

In this paper we extend the guaranteed cost control approach for nonlinear quadratic systems (NLQSs), developed by the same authors in some recent papers, to the stochastic framework. In particular, we consider a stochastic NLQS in the Itô's form and provide a sufficient condition for the existence of a state feedback controller guaranteeing, with a certain risk factor α E[0,1), that the closed loop system satisfies, for any initial condition belonging to a given polytopic set, an assigned bound for a given quadratic cost; the condition requires to solve a feasibility problem constrained by linear matrix inequalities. The proposed theory is then illustrated by an example concerning the design of optimal strategies for the removal of malicious software in computer networks.