Higher-order continuous-time implicit systems: Consistency and weak consistency, impulse controllability, geometric concepts, and invertibility properties (Q1923216)

This paper considers smooth and distributional solutions of linear time-invariant systems \[ A_k x^{(k)}(t)+\cdots + A_0 x(t)=Bu(t). \] Weak consistency of degree \(m\) is defined in such a way that weak consistency of degree 0 coincides with the standard concept of consistency and the highest degree of weak consistency is impulse controllability. Maximal weak consistent subspaces of each degree are characterized in terms of the system coefficients. In addition, impulse controllability, and left and right invertibility are considered.