The persistence of impulse controllability

Differential-algebraic systems are generically controllable and stabilizable

“…Banaszuk and Przyłuski [1] consider an algebraic criterionwhich they do not justify analytically and which is not related to any concept of controllability-and give a sufficient condition so that the set of systems satisfying the algebraic criterion contains an open and dense subset. The second contribution is by Belur and Shankar [3].…”

“…This approach was used by Belur and Shankar in their investigations of genericity of impulse controllable systems (see [3,Section 3]). Since they consider differentialalgebraic equations described by differential operator matrices and hence an infinite dimensional vector space, they need to extend the definition of generic sets to this space using the limit topology of the Zariski topology.…”