Model Reduction of Stochastic and Deterministic Continuous Time Linear Systems (Lypunov Equation, Schawrz Approximation).

Two new approaches for reducing the order of large scale continuous systems are presented. The first approach is a modified version of the aggregation technique. It uses the matching properties of the steady state output covariance and the Markov parameters of the high order system to those of the r(\u27th) order model. This approach also uses a new algorithm derived for the computation of the controllability and observability Grammians, to produce controllable, observable and stable low order models. These is no unique method available for evaluating the aggregation matrix or the matrix relating the system state vector to the model state vector. A procedure, based on the singular value decomposition of the controllability Grammian of the system, is provided for the computation of the aggregation matrix. This approach is also extended to design low order deterministic continuous time varying linear models. The second approach in this dissertation is an improved version of the Schwarz approximation. It uses the Schwarz canonical form to insure the stability of the model, the impulse response energy to determine the order of the model, the singular values or the second order modes of the controllability Grammian to select the state variables to be retained in the model, and the time moment matching properties to reduce the steady state errors between the response of the model and that of the system. This dissertation also introduces an algorithm for the computation of the frequency responses of the system and/or the model. This algorithm does not require any complex arithmetic, which is a major problem for most compliers; it is simple and easy to implement in a small computer