$(A,\mathcal{B})$-Invariant Distributions and Disturbance Decoupling of Nonlinear Systems

The concept of $(A,B)$-invariant subspaces has resulted in a unified approach to many of the basic structural properties of time-invariant linear systems (W. M. Wonham, Lecture Notes in Economics and Mathematical Systems, vol. 101, Springer-Verlag, New York, 1974). The purpose of this paper is to introduce the more general notion of $(A,\mathcal{B})$-invariant distributions on differentiable manifolds and to use this idea to study the disturbance decoupling problem for a class of nonlinear systems which evolve on real analytic manifolds.