Nonlinear worst case (H∞) control

I previously (1994) presented necessary and sufficient conditions for the existence of worst case controllers and estimators for nonlinear systems. These are also called H_∞ suboptimal controllers and estimators. I considered affine and more general nonlinear systems, both time varying and autonomous over finite, semi-infinite and infinite intervals. In particular, I gave necessary and sufficient conditions for the solvability of a standard H_∞ suboptimal control problem by measurement feedback that involve the solvability of a pair of partial differential equations of the Hamilton-Jacobi type. The first one is the one associated with the problem of H-infinity suboptimal control by state feedback that has appeared previously in the work of several authors. The second one is a new Hamilton-Jacobi equation associated with H_∞ suboptimal estimation. I summarize some of these results in this paper