A controllability test for general first-order representations (Q1354856)

The paper contains results on controllability for generalized linear finite-dimensional control systems with constant coefficients. Since the mathematical model presented in the paper is purely algebraic, both discrete and continuous systems can be considered. Using methods of linear algebra, the form of the generalized controllability matrix is given. Then, a necessary and sufficient rank condition for controllability is formulated and proved using different types of linear transformations in the state space. The space of reachable states is also defined using the concept of controllability matrix. Two simple illustrative numerical examples are also given. Moreover, the relationships to the existing results on controllability for generalized systems are discussed. Similar controllability problems for generalized systems can be found in the paper [\textit{J. C. Willems}, IEEE Trans. Autom. Control 36, No. 3, 259-294 (1991; Zbl 0737.93004)].