The local disturbance decoupling problem with stability for nonlinear systems

In this paper the Disturbance Decoupling Problem with Stability (DDPS) for nonlinear systems is considered. The DDPS is the problem of finding a feedback such that after applying this feedback the disturbances do not influence the output anymore and x = 0 is an exponentially stable equilibrium point of the feedback system. For systems that can be decoupled by static state feedback it is possible to define (under fairly mild assumptions) a distribution Δs* which is the nonlinear analogue of the linear V*s, the largest stabilizable controlled invariant subspace in the kernel of the output mapping, and to prove that the DDPS is locally solvable if and only if the disturbance vector fields are contained in Δs*.