H(infinity) Control of Nonlinear Systems: A Class of Controllers

Abstract The standard state space solutions to the Em control problem for linear time invariant systems are generalized to nonlinear time-invariant systems. A class of nonlinear -controllers are parameterized as nonlinear fractional transformations on contractive, stable free nonlinear parameters. As in the linear case, the E, control problem is solved by its reduction to four simpler special state space problems, together with a separation argument. Another byproduct of this approach is that the sufficient conditions for control problem to be solved are also derived with this machinery. The solvability for nonlinear H infinity-control problem requires positive definite solutions to two parallel decoupled Hamilton-Jacobi inequalities and these two solutions satisfy an additional coupling condition. An illustrative example, which deals with a passive plant, is given at the end.