H∞ control of nonlinear systems via output feedback: a class of controllers

The standard state space solutions to the H_∞ control problem for linear time invariant systems are generalized to nonlinear time-invariant systems. A class of nonlinear H_∞ controllers are parametrized as nonlinear fractional transformation on contractive, stable free nonlinear parameters. As in the linear case, the H_∞ control problem is solved by its reduction to a state feedback and output injection problems, together with a separation argument. the sufficient conditions for H_∞-control problem to be solved are also derived with this machinery. The solvability for nonlinear H_∞ control problem requires positive definite solution to two parallel decoupled Hamilton-Jacobi inequalities and these two solutions satisfy and additional coupling condition. An illustrative example, which deals with a passive plant, is given