Controllability And Observability Of Nonlinear Systems

Two of the fundamental concepts appearing in the earlier studies on linear control systems are controllability and observability. In particular, it was through the work of R.E. Kalman that the notion of controllability of a linear system was shown to be of interest in itself, and not only as it was appearing in the context of optimal control. Linear controllability turns out to be of importance in many contexts, with perhaps as one of the most useful applications, feedback stabilization or rather pole placement through state feedback. On the other hand, controllability has a very simple and appealing formulation in that a linear control system is said to be controllable if for any given pair of initial and final states there exists an input function that ‘steers’ the system from initial to final state.