Nonlinear \(H_ \infty\) almost disturbance decoupling (Q1337659)

Disturbance decoupling is the problem of finding a compensator such that the disturbance has no influence on the output of a given system. By the adjective ``almost'' one denotes the weaker problem of making this influence arbitrarily small. Here, the almost disturbance decoupling problem is related to the \(H_ \infty\) problem. The authors solve the almost disturbance decoupling problem for a class of nonlinear systems. Sufficient conditions are given provided that the control and disturbance enter the system linearly. Formulas for the controller that makes the ratio between the \(L^ 2\)-norm of the output less than a given number times the \(L^ 2\)-norm of the disturbance are given as well. Furthermore, they obtain a necessary condition for the solvability of the almost disturbance decoupling problem with stability. This last problem is a special \(H_ \infty\) problem.