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Minimal controllability problems on linear structural descriptor systems
We consider minimal controllability problems (MCPs) on linear structural
descriptor systems. We address two problems of determining the minimum number
of input nodes such that a descriptor system is structurally controllable. We
show that MCP0 for structural descriptor systems can be solved in polynomial
time. This is the same as the existing results on typical structural linear
time invariant (LTI) systems. However, the derivation of the result is
considerably different because the derivation technique of the existing result
cannot be used for descriptor systems. Instead, we use the Dulmage--Mendelsohn
decomposition. Moreover, we prove that the results for MCP1 are different from
those for usual LTI systems. In fact, MCP1 for descriptor systems is an NP-hard
problem, while MCP1 for LTI systems can be solved in polynomial time