On the design of a reduced-order H∞ controller for nonlinear sampled-data systems

In this paper, the problem of designing reduced-order H-infinity controllers is studied for nonlinear continuous-time systems with sampled measurements. Using the concepts of dissipativity and differential game, sufficient conditions are derived for the existence of such reduced-order H-infinity 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 those used in the construction of full-order H-infinity controllers. When these conditions hold, state-space formulae are also given for such reduced-order controllers. An illustrative example is also included.