H∞ controller reduction for nonlinear sampled-data systems

In this paper, the problem of designing reduced-order H^∞ controllers is studied for nonlinear continuous-time systems with sampled measurements. Using the concepts of dissipativity and differential gain, sufficient conditions are derived for the existence of such reduced-order H^∞ controllers. These conditions are expressed in terms of the solutions of two Hamilton-Jacobi inequalities, comprising a standard Hamilton-Jacobi inequality and a differential Hamilton-Jacobi inequality with jumps. These Hamilton-Jacobi inequalities are exactly the one used in the construction of full-order H^∞ controllers. When these conditions hold, state-space formulae are also given for such reduced-order controllers.