An interesting type of distributed system is a collection of identical subsystems that interact in a distinct pattern. A notable example is a ring, more commonly referred to as a circulant system. It is well known that control problems for circulant systems can be simplified by exploiting their common connection with the shift operator. Based on an examination of the algebraic properties underlying this connection, we identify a broader class of systems that share common base transformations. We call it the class of linear patterned systems. Members with meaningful physical interpretations include symmetric circulant systems, triangular Toeplitz systems and certain hierarchical systems. A geometric approach is employed to study the basic control properties of patterned systems, including controllability, observability and decomposition. Controller synthesis for several stabilization problems is then considered, and we show that a patterned solution to the problems exists if a general solution exists.

An interesting type of distributed system is a collection of identical subsystems that interact in a distinct pattern. A notable example is a ring, more commonly referred to as a circulant system. It is well known that control problems for circulant systems can be simplified by exploiting their common connection with the shift operator. Based on an examination of the algebraic properties underlying this connection, we identify a broader class of systems that share common base transformations. We call it the class of linear patterned systems. Members with meaningful physical interpretations include symmetric circulant systems, triangular Toeplitz systems and certain hierarchical systems. A geometric approach is employed to study the basic control properties of patterned systems, including controllability, observability and decomposition. Controller synthesis for several stabilization problems is then considered, and we show that a patterned solution to the problems exists if a general solution exists.

Thesis (M. Phil.)--University of Hong Kong, 2008. / Also available in print.

Thesis (Ph.D.) - University of Glasgow, 2008. / Ph.D. thesis submitted to the Faculty of Information and Mathematical Sciences, Department of Mathematics, University of Glasgow, 2008. Includes bibliographical references. Print version also available.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 74-76). Also available in electronic version. Access restricted to campus users.

Thesis (M. Eng.), Memorial University of Newfoundland, 1999. / Bibliography: leaves 118-119.

Thesis (Ph. D.)--Brigham Young University. Dept. of Mathematics, 2005. / Includes bibliographical references (p. 113-114).

Thesis (M.A.)--University of North Carolina at Wilmington, 2006. / Includes bibliographical references (leaf: [41])

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Made available in DSpace on 2014-06-11T19:23:31Z (GMT). No. of bitstreams: 0 Previous issue date: 2002-08-30Bitstream added on 2014-06-13T20:30:18Z : No. of bitstreams: 1 castro_alp_me_prud.pdf: 5444410 bytes, checksum: 7e68cc5dce3b24fd2a1e82437186ffef (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / O posicionamento através do GPS alterou profundamente a metodologia geodésica nas últimas décadas. Atualmente, as aplicações dessa técnica espacial não se limita à determinação das coordenadas geodésicas como ocorria no posicionamento clássico. O posicionamento por GPS, combinado com um modelo geoidal, proporciona a altitude ortométrica, com a precisão suficiente para várias aplicações cotidianas (mapeamento, distribuição de água, saneamento básico, irrigação, planejamento urbano, etc). Isto significa que, nessas aplicações, já é possível substituir o nivelamento tradicional pelo nivelamento por satélite com a simplicidade oferecida pelo GPS. Os objetivos principais deste trabalho, em síntese, são os seguintes: determinar a altitude ortométrica num conjunto de Referências de Nível combinando o posicionamento por GPS com um modelo geoidal do Estado de São Paulo; avaliar o nivelamento através do GPS, comparando as altitudes determinadas com as conhecidas nesses pontos; e definir estratégias para adequar o nivelamento por satélite às aplicações cotidianas. A metodologia proposta consiste em avaliar o nivelamento realizado com o GPS, por meio da análise estatística das discrepâncias entre as altitudes ortométricas determinada e conhecida em cada ponto; e definir estratégias de observação e processamento de dados GPS visando essas aplicações. Os resultados obtidos neste trabalho mostram que é possível realizar o nivelamento por satélite utilizando receptores GPS equipados com antenas de duas freqüências ou mesmo de uma freqüência e bases de comprimento até 250 km. Assim, o usuário possui alternativa para substituir o nivelamento convencional pelo nivelamento por satélite, com os benefícios da simplicidade operacional, da rapidez e do baixo custo que o GPS oferece. / The GPS positioning has deeply modified the geodetic methodology in the last decades. Currently, the applications of this space technique are not limited to the determination of the geodetic coordinates as it happened in classical positioning. The GPS positioning, combined with a geoidal model, provides the orthometric heights, with the enough precision for some daily applications (mapping, water distribution, basic sanitation, irrigation, urban planning, etc). In these applications, it is already possible to substitute the traditional levelling by the satellite levelling with the simplicity allowed by the GPS. The main objectives of this work are the following: to determine the orthometric heights in a set of leveling benchmarks by combining the GPS positioning and a gravimetric geoidal model in São Paulo state; to evaluate the GPS levelling, by comparing the obtained orthométric heights with the known ones at these points; and to define strategies to applay the satellite levelling to the daily applications. The proposed methodology consists in evaluating the GPS levelling through the statistical analysis of the discrepancies between the determined orthometric heights and the known one at each point; and to recomend strategies for observation and data processing. The results obtained in this work show that, for many applications, the GPS levelling can be accomplished, by using GPS receivers equipped with two frequencies, or even one frequency antennas, for baselines up to 250 km. So the user has an alternative to substitute the conventional levelling by the satellite levelling, with the benefits of operational simplicity, the little time consuming, and the low cost enabled by using GPS.