H∞ for nonlinear stochastic systems

In this paper we develop a H_∞ type theory, from the dissipation point of view, for a large class of time-continuous stochastic nonlinear systems. In particular, we introduce the notion of stochastic dissipative systems analogously to the familiar notion of dissipation associated with deterministic systems am utilize it as a basis for the development of our theory. Having discussed certain properties of stochastic dissipative systems, we consider time-varying nonlinear systems for which we establish a connection between what is called the L₂-gain property and the solution to a certain Hamilton-Jacobi inequality (HJI), that may be viewed as a bounded real lemma for stochastic nonlinear systems. The time-invariant case with infinite horizon is also considered, where for this case we synthesize a worst case based stabilizing controller. Stability in this case is taken to be in the mean-square sense. In the stationary case, the problem of robust state-feedback control is considered in the case of normbounded uncertainties. A solution is then derived in terms of linear matrix inequalities.