Global Decompositions of Control Systems

Abstract

In the previous Chapter, we have shown that a nonsingular and involutive distribution Δ induces a local partition of the state space into lower dimensional submanifolds and we have used this result to obtain local decompositions of control systems. The decompositions thus obtained are very useful to understand the behavior of control systems from the point of view of input-state and, respectively, state-output interaction. However, it must be stressed that the existence of decompositions of this type is strictly related to the assumption that the dimension of the distribution is constant at least over a neighborhood of the point around which we want to investigate the behavior of our control system.