In this paper the basic properties of the singular value decomposition (SVD) for integral equation models of distributed parameter systems (DPS) are presented in the context of process identification and model-based control. In addition, new methods of analysis and computation are described in which SVD-based techniques are used to provide a practical solution for the DPS identification and control problem. Once developed, these novel procedures are applied to a class of linear DPS which are conventionally described by parabolic partial differential equation (PDE) models. An alternative integral equation representation for these processes is used to provide a general and readily identifiable pseudo-modal input/output model for a wide variety of such DPS, including both spatially self-adjoint (diffusive) and non-self-adjoint (convective/diffusive) systems It is demonstrated that this SVD-based internal equation model of DPS is a sound and convenient basis for pseudo-modal feedback control system designs. A later paper will extend these methods to allow for model-predictive controller designs and nonlinear DPS