Robust state-feedback ℋ∞ control of nonlinear systems under matching conditions

In this paper, the problem of disturbance attenuation with internal stability for uncertain nonlinear systems satisfying certain matching conditions is considered. The uncertainties are assumed to be due to both parametric and higher order nonlinearities neglected as modelling errors. It is shown that this problem is solvable if there exist a smooth positive semi-definite function satisfying a certain Hamilton-Jacobi-Isaacs equation (inequality) with some appropriate scaling function. Furthermore, it is shown that if this solution exists, it represents a Lyapunov function for the closed-loop nonlinear system