The Hautus Test and Genericity Results for Controllable and Uncontrollable Behaviors

This paper generalizes the classical Hautus Test to systems described by partial differential equations

Controllability and Vector Potential: Six Lectures at Steklov

Kalman's fundamental notion of a controllable state space system, first described in Moscow in 1960, has been generalised to higher order systems by J.C.Willems, and further to distributed systems defined by partial differential equations. It turns out, that for systems defined in several important spaces of distributions, controllability is now identical to the notion of vector potential in physics, or of vanishing homology in mathematics. These lectures will explain this relationship, and a few of its consequences. It will also pose an important question: does a controllable system, in any space of distributions, always admit a vector potential? In other words, is Kalman's notion of a controllable system, suitably generalised, nothing more - nor less - than the possibility of describing the dynamics of the system by means of a vector potential?Comment: This version includes subject inde