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The exact parameter values of mathematical models are often uncertain or evenunknown. Nevertheless, we may have access to crude information about theparameters, e.g., that some of them are nonzero. Such information can becaptured by so-called pattern matrices, whose symbolic entries are used torepresent the available information about the corresponding parameters. In thispaper, we focus on pattern matrices with three types of symbolic entries: thosethat represent zero, nonzero, and arbitrary parameters. We formally define andstudy addition and multiplication of such pattern matrices. The results arethen used in the study of three strong structural properties, namely,controllability of linear descriptor systems, and input-state observability andoutput controllability of linear systems.

Properties of pattern matrices with applications to structured systems