Patterned Linear Systems and Control

A method to characterize the symmetries inherent within physical systems via automorphism groups has already been established. In this thesis, we elaborate on this method and define a special reduced form to which the system matrices of a linear system can be decomposed based on these inherent patterns. We employ this decomposition and the resulting block diagonal form to adapt basic control theory concepts such as controllability and stabilizability to a pattern-preserving framework. We give a pole placement algorithm that synthesizes a feedback matrix that is constrained by the patterns of the system. Moreover, we apply our patterned framework to traditional control problems such as stabilization by measurement feedback and output stabilization, and give pattern-preserving feedback synthesis procedures for these problems. Finally, we provide a set of computational tools that can be used to nd the aforementioned decomposition and generate pattern-preserving feedbacks for a given patterned system.M.A.S