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Recently, the concept of strong structural controllability has attracted renewed attention. In this context the existing literature to strong structural controllability has been revisited and some of the previous results have been found to be incorrect. Therefore, in this paper an overview of the previous results on strong structural controllability, counterexamples and a new graph-theoretic characterization of strong structural controllability are given.

Abstract-In this note we consider continuous-time systemsẋ(t) = A(t)x(t) + B(t)u(t), y(t) = C(t)x(t) + D(t)u(t) as well as discrete-time systems x(t + 1) = A(t)x(t) + B(t)u(t), y(t) = C(t)x(t) + D(t)u(t) whose coefficient matrices A, B, C and D are not exactly known. More precisely, all that is known about the systems is their nonzero pattern, i.e., the locations of the nonzero entries in the coefficient matrices. We characterize the patterns that guarantee controllability and observability, respectively, for all choices of nonzero time functions at the matrix positions defined by the pattern, which extends a result by MAYEDA and YAMADA for time-invariant systems. As it turns out, the conditions on the patterns for time-invariant and for timevarying discrete-time systems coincide, provided that the underlying time interval is sufficiently long. In contrast, the conditions for time-varying continuous-time systems are more restrictive than in the time-invariant case.Index Terms-MSC: Primary, 93B05; Secondary, 93B07, 93C05, 15A03, 05C50.

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