The state augmented system: Theory and applications to linear quadratic cost functional problem

A linear dynamic controller (LDC) or compensator and a linear dynamic plant can always be modeled as a Plant-Controller State-Augmented System (SAS). The key feature which distinguishes two Plant-Controller SAS's is the prescribed criteria, e.g., stabilizing the plant, meeting required phase margin or gain margin, minimizing a cost functional associated with the Plant-Controller SAS, etc. In this dissertation we develop a theory for Plant-Controller SAS and investigate its applications to the LQ cost functional problems.;We begin by defining and showing the existence of a SAS. Controllability and observability are then discussed. The frequency shaping effect of state-augmented method in LQ cost functional problems will be studied. The notion of an Augmented Steady State Riccati Equation (AUSSRE) is defined, and relationships between it and the Steady State Riccati Equation (SSRE) will also be studied. This includes the role plays by the initial states of the LDC in the LQ problems.;Next, we show that an observer and a linear plant can be modeled as a Plant-Controller SAS. We also show that given a Plant-Controller SAS and define $J=intsbsp{0}{infty}Vert v-xVertsp2dt