Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2008. / Includes bibliographical references (leaves 103-114). Also available in electronic version.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1957. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves [90]-100).

Thesis (M.S.)--University of Wisconsin--Madison. / Typescript. eContent provider-neutral record in process. Description based on print version record.

Thesis (M. Sc.)--University of Canterbury, 2006. / Typescript (photocopy). Includes bibliographical references (p. 125-133). Also available via the World Wide Web.

A thorough review of the literature on the model reduction of linear, time-invariant, dynamical systems in both the frequency and time domains is presented. Particular attention is paid to the least-squares extension of the classical method of Padé approximation. An account is given of the development of apparently different approaches of least-squares parameter- matching Padé model reduction applied to continuous-time and discrete-time systems. These approaches are shown to be related via a unifying theory. From the formulation it is possible to show several interesting features of the least-squares approach which lead to a fuller understanding of exactly how the reduced model approximates the full system. An error index is derived in the general continuous-time case and it is shown that a range of system parameter preservation options are available. Using the theory developed in the continuous-time case a non-uniqueness property of the method is proven. An ‘optimal’ least-squares method based on the approach and the introduction of weighting for the system parameters are both investigated. The unifying theory is extended to the discrete-time case where an important new stability preservation property is proved and is shown to provide the basis for a new least- squares Padé method. This method uses transformations between the z- and 5-planes to guarantee stable reduced order models approximating stable high order continuous-time systems. The application of least-squares Padé approximation is further extended to the multivariable case with particular attention given to the factors affecting the levels of order reduction achieved. Appropriate numerical examples are used to illustrate the main points of the thesis and graphs of the impulse and step responses are used throughout to visually highlight the accuracy of approximation.

Please read the abstract in the front section of this document / Dissertation (MSc (Mathematics))--University of Pretoria, 2005. / Mathematics and Applied Mathematics / unrestricted

A new approach to the identification problem of linear continuous-time time-invariant systems from input-output measurements is presented. Both parametric and nonparametric system models are considered. The new approach is based on the use of continuous-time functions, the modal functions, defined in terms of the system output, the output derivatives and the state variables under the assumption that the order n of the observable system is known a priori. The modal functions are obtained by linear filtering operations of the system output, the output derivatives and the state variables so that the modal functions are independent of the system instantaneous state. In this case, the modal functions are linear functions of the input exponential modes, and they contain none of the system exponential modes unlike the system general response which contains modes from both the system and the input. The filters parameters, the modal parameters are estimated using linear regression techniques. The modal functions and the modal parameters of the output and its derivatives are used to identify parametric input-output and state models of the system. The coefficients of the system characteristic polynomial are obtained by solving n algebraic equations formed from the estimates of the modal parameters. Estimates of the parameters associated with the system zeros are obtained by solving another set of linear algebraic equation. The system frequency response and step response are estimated using the output modal function. The impulse response is obtained by filtering the estimated step response using the output first derivative modal parameters. A new method is presented to obtain the system poles as the eigenvalues of a data matrix formed from the system free response. The coefficients of the system characteristic polynomial are obtained from the data matrix through a simple recursive equation. This method has some important advantages over the well known Prony's method. The state modal functions are used to obtain a minimum-time observer that gives the continuous-time system state as a direct function of input-output samples in n sampling intervals. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

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