Inverse optimal design of input-to-state stabilizing nonlinear controllers

We show that input-to-state stabilizability is both necessary and sufficient for the solvability of a Hamilton-Jacobi-Isaacs equation associated with a meaningful differential game problem similar to, but more general than, the "nonlinear H/sub /spl infin//" problem. The significance of the result stems from the fact that constructive solutions to the input-to-state stabilization problem are available. Rather than completion of squares, the main tools in our analysis are Legendre-Fenchel transformations and the general form of Young's inequality.