On the stability of the information state system (Q1350968)

The purpose of this paper is to present some preliminary results on the stability of the information state system. The information state system underlies the (infinite-dimensional) dynamics of an \(H_\infty\) controller for a nonlinear system. Thus it is important to understand its stability and the structure of its equilibrium points. We analyse the important case corresponding to the mixed sensitivity problem. We prove the existence of an equilibrium information state, convergence under very general conditions to such an equilibrium state \(p_e\) and uniqueness of this state (up to an irrelevant constant).