Graph theoretic and boolean conditions for structurally fixed modes of augmented system forms

The structurally fixed modes are studied for systems with state and output feedback and outputs which generally influence the system and measure states and inputs. Conditions for structurally fixed modes are produced and are compared with the subsystem unreachability. A condition on the graph of the augmented system and a condition based on the decomposition of the reduced x-dimensional system are thus established for this form of LTI augmented systems.