Design method for an adaptive robust controller with L2-gain disturbance attenuation for nonlinear systems with uncertainty

A nonlinear feedback control design for the adaptive robust H_∞ control problem for nonlinear systems with gain bounded uncertainty is presented. An existing control scheme developed for nonlinear systems with relative degree of one is extended to the case where nonlinear systems have general relative degree. A Lyapunov function is constructed that ensures not only the stability of the closed-loop system but also satisfies the dissipation inequality ensuring L₂-gain performance. Then the controller can be obtained by the recursive use of the existing control scheme. A closed-form solution for the nonlinear H_∞ control problem is provided without using a Hamilton-Jacobi inequality in the general relative degree case. Sufficient conditions which nonlinear systems should satisfy for solvability of the problem are provided.