In this note, we investigate structural controllability of networked systems in which subsystems have high-order and heterogeneous dynamics and are coupled through relative state variables. It is aimed to search conditions for subsystem dynamics, under which structural controllability of the whole network essentially depends only on network topology as well as subsystem interconnection links. Necessary and/or sufficient conditions for structural controllability are given by simplifying subsystem dynamics. As an application, these criteria are utilized to design network topology that minimizes the number of subsystem interconnection links under the requirement of structural controllability without concerning subsystem dynamics, which is also much more efficient computationally than a direct design for the global system. The effectiveness of the criteria is demonstrated through several examples.
In this paper, we consider the controllability and observability of generalized linear time-varying (LTV) systems whose coefficients are not exactly known. All that is known about these systems is the placement of non-zero entries in their coefficient matrices (A, B). We provide the characterizations in order to judge whether the placements can guarantee the controllability/observability of such LTV systems, regardless of the exact value of each non-zero coefficient. We also present a direct and efficient algorithm with an associated time cost of O(n + m + ν) to verify the conditions of our characterizations, where n and m denote the number of columns of A and B, respectively, and ν is number of non-zero entries in (A, B).
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