THEORY OF MATRIX

Author: TARRAGONA ROMERO SONIA.
Year: 2004.
University: POLITÉCNICA DE CATALUÑA [www.upc.edu].
Place of defense: AULA CAPELLA - ETSEIB.
Place of preparation: U FACULTAT DE MATEMATIQUES I ESTADISTICA SUD.

Author: ROMERO REY GREGORIO.
Year: 2005.
University: POLITÉCNICA DE MADRID [www.upm.es].
Place of defense: E.T.SUP. INGENIEROS INDUSTRIALES.
Place of preparation: E.T.S.I. INDUSTRIALES.

Summary: Efforts in the automated method Bond-Graph in recent years focused on solving the problem of the coordinates that appear frequently dependent on the mechanical systems, electrical and thermal. The development of this thesis is focused on providing a causal allocation algorithm specially designed to allow maximum freedom to modeler, but it will have to worry about the resolubilidad or not the system, and without having to take any decision that might affect the final calculation, so as to solve our problems in the simulation models with differential causality without having to modify the chart graph. In addition, it reduces the maximum set of differential equations necessary to carry out the simulation through the elimination of algebraic equations system DAEs in cases where possible. This will decrease the time of computation used in the simulation. Moreover, we propose a method for the automatic generation of optimized and the equations of state necessary for the analysis of linear and nonlinear systems, made by the technique of Bond-Graph. Construction of these equations is performed using techniques of symbolic computation. This will have the equations of the system in a format that facilitates its subsequent use to solve problems or sensitivity optimization. This method takes into account both the non-linearities geometric presenting mechanical systems (discussed by elements transformer and gyrator reason variable), as the non-linear behavior of elementary building blocks (inertia, and resistance springs). Finally, in order to demonstrate the effectiveness of proposed algorithms, has developed a code for the simulation of dynamic systems using the technique of Bond-Graph in Windows environment, which implements the proposals along the thesis and modeling enables both combined using graphs, functions, variables and conditional sentences, as the presentation of differential equations and algebraic end in a symbolic way, all in a friendly environment and allowing postprocesar easily the results of simulations made without having to perform after a compilation.

Author: MARCAIDA BENGOECHEA SILVIA.
Year: 2005.
University: PAÍS VASCO [www.ehu.es].
Place of defense: FACULTAD DE CIENCIA Y TECNOLOGÍA.
Place of preparation: FACULTAD DE CIENCIA Y TECNOLOGÍA.

Summary: This thesis tries to be an example of how the close relationship between systems and linear arrays polynomial used to fertilize both fields. More specifically: 1, - were unified under the name of polynomial matrix representation of a linear system controllable different concepts that appear in the literature. 2-apply properties of the matrix structure in polynomial to assign infinity to a system in open loop. 3-polynomial representations are used to establish a matrix homeomorphism between the two orbits following spaces: the systems controllable under the action of the similarity of parent and the degree of polynomial with fixed decisive action by the group's parent unimodulares on the right with the topology compacto-abierta. Thus, the latter space inherits all the topological properties of the former, which have been widely studied. 4-homeomorphism used along with results of previous disturbance arrays and systems to learn how to change the structures and Wiener-Hopf of finite arrays polynomial under small perturbations. In addition, it also examines the variation in structure to disrupt slightly infinite matrix polynomial with reverse itself using the results of disturbance beam arrays already known.