Digraph characterization of structural controllability for linear descriptor systems (Q1372972)

Linear, time-invariant, continuous-time descriptor control systems are considered. Using graph-theoretical methods different kinds of controllability are analyzed. Based on the concept of structural matrix, necessary and sufficient conditions for structural controllability are formulated and proved. Next, structural impulse controllability and structural \(r\)-controllability are investigated, and criteria for them are derived. Moreover, these results are compared with the structural controllability results which are known in the literature. Finally, a nontrivial numerical example (taken from electrical engineering) illustrates the application of the theoretical results. It should be pointed out that controllability of descriptor control systems has been considered in the paper [\textit{D. Cobb}, IEEE Trans. Autom. Control AC-29, 1076-1082 (1984)].