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Model order reduction (MOR) is one of the general techniques in the fields of computeraided design (CAD) and electronic design automation (EDA) which accelerates the flow of electronic simulations and verifications. By MOR, the original circuit, which is described by a set of ordinary differential equations (ODEs), can be trimmed into a much smaller reduced-order model (ROM) in terms of the number of state variables, with approximately the same input-output (I/O) characteristics. Hence, simulations using this ROM will be much more efficient and effective than using the original system. In this thesis, a novel and fast approach of computing the projection matrices serving high-order Volterra transfer functions in the context of weakly and strongly nonlinear MOR is proposed. The innovation is to carry out an association of multivariate Laplace-domain variables in high-order multiple-input multiple-output (MIMO) transfer functions to generate univariate single-s transfer functions. In contrast to conventional projection-based nonlinear MOR which finds projection subspaces about every si in multivariate transfer functions, only that about a single s is required in the proposed approach. This translates into much more compact nonlinear ROMs without compromising accuracy. Different algorithms and their extensions are devised in this thesis. Extensive numerical examples are given to prove and verify the algorithms. / published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

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Ph.D. / The work presented in this dissertation is concerned with the application of Chaos Theory to the field of Electrical and Electronic Engineering. A comprehensive study on electrical and electronic systems which exhibit chaotic behaviour, forms an integral part of this work. The objective of this survey is, firstly, to assess how widely chaos occurs in the field of electrical engineering. Secondly, the survey attempts to determine how successfully chaotic behaviour (in electrical systems) is identified and characterized. Finally, the survey aims to determine to what extent nonlinear phenomena and specifically chaos is applied to solve engineering problems. From this survey it is concluded that the study of chaos in electronics has reached a mature state. Currently, research focuses on controlling chaos, finding new applications of chaos as well as using chaos theory to gain a better understanding of the nonlinear world we live in. The other component of this dissertation consists of research done in the field of electronics. Contributions are made in controlling chaos and the analysis of chaotic systems both analytically and numerically.

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