H∞ controller design for nonlinear system

A solution to the Riccati equation is investigated for the class of multi-variable separable nonlinear systems where the output of the nonlinear element is a function of control input-signal amplitude and frequency. The analytical dependency of the H_∞ Riccati solution to the amplitude of the nonlinearity is examined. The formulas of Li and Chang are used to synthesize the H_∞ controller. The dynamical controller is constructed based on the solutions to the two Riccati equations which are also functions of the amplitude of the nonlinearity. The closed loop stability and system performance are analyzed. A key contribution of this paper is that it deals with the nonlinearity of the system with an H_∞ approach. Of the particular interest is the application of H_∞ to the nonlinear systems with delay