H∞ controller reduction for general nonlinear sampled-data systems

This paper is concerned with the problems of designing reduced-order H^∞ controllers for nonaffine nonlinear continuous-time systems with sampled measurements. We propose sufficient conditions for the existence of such reduced-order H^∞ controllers using the concepts of dissipativity and differential game. These conditions are expressed in terms of the solutions of two Hamilton-Jacobi inequalities which comprising a standard Hamilton-Jacobi inequality and a differential Hamilton-Jacobi inequality with jumps. When these conditions hold, we also give a state-space formulae for such reduced-order controllers.