Simultaneous H∞ control for a collection of nonlinear systems in canonical form

A constructive method for designing simultaneous H^∞ controllers for a class of nonlinear control systems is developed. Under mild assumptions, it is shown that control storage functions (CSFs) for nonlinear systems in canonical form can be constructed systematically; and, simultaneous H^∞ control for such systems can always be achieved. Based on the derived CSFs, a universal formula for constructing simultaneous H^∞ controllers is proposed explicitly. An illustrative example is given to show the validity of the method.