Properties of Pattern Matrices With Applications to Structured Systems

In cases where we do not have the exact parameter values of a mathematical model, often at least some structural information, e.g., that parameters are nonzero. Such information can be captured by so-called pattern matrices, whose symbolic entries used to represent available about corresponding parameters. this letter, focus on matrices with three types entries: those zero, nonzero, and arbitrary We formally define study addition multiplication such matrices. The results then in algebraic characterization strong properties. particular, provide sufficient conditions for controllability linear descriptor systems, necessary input-state observability, output systems.