Solvability, controllability, and observability of singular systems (Q792928)

The problems of solvability, controllability, and observability for the singular system \(K\dot x(t)=Ax(t)+Bu(t)\) are studied, where K is a singular, square matrix and u(t) is a complex vector function sufficiently differentiable. The classical theories of matrix pencils are first related to the singular systems solvability. Then, the concepts of reachability, controllability, and observability of regular systems are extended to singular systems. Finally, the set of reachable states is described. The proposed matrix conditions for testing the controllability and observability for singular systems are simple and always feasible.