Center manifold and H∞ control in weak nonlinear systems

In this paper, we describe the sufficient condition which confines the solutions of weak nonlinear simultaneous differential equations to a stable center manifold. The obtained conditions are used for deriving the solution of a weak nonlinear H^∞ regulator problem. By using a solution of the Ricatti equation, the sufficient conditions for obtaining the feedback law are derived from the result of studying the center manifold. Moreover, by using a Lyapunov function, we evaluate whether the closed loop system given by this feedback law is stable or not