Generalized Inverse of Redundant LTI Systems

This thesis investigated the framework of the generalized inverse design for the redundant linear systems. The novel theories given in this thesis can help people to better understand the properties of the generalized inverse, especially for the Schatten norm of the inverse and the redundancy in the row/column norm constrained inverse design. The new theories explain some findings in previous research, and these common features in minimized H₂ and H_∞ norm inverses can be further expanded to the whole minimized Schatten p norm cases. The availability of the inverse design with row/column norm constraint are thoroughly discussed. Under the guidelines of this theory,the minimized row/column H₂ norm inverse design frameworks are separately presented for causal and noncausal systems in this thesis.