Algoritmos paralelos para la reducción de sistemas lineales de control estables

[EN] In the field of control theory, sometimes system models of big size (with many state variables) appear. When one of these high order systems needs to be simulated, studied or controlled, it is convenient to perform a previous work of model reduction in order to reduce the necessary (economic and temporal) costs. This process of obtaining a low order adequate representation of the original system usually has a high cost, because it has to be done with the original unreduced system. Thus, it is important to have high performance implementations for the problem of reducing linear control systems. In this thesis high performance implementations for some methods of model reduction have been developed. Current algorithms for model reduction of stable linear control systems and their implementation in the control library SLICOT have been analysed. New parallel algorithms for the methods strongly based on solving Lyapunov equations have been proposed. The new developed routines are incorporated in the high performance library for control PSLICOT. Apart from the main functions in charge of model reduction, all operations appearing in the problem and not having a high performance version yet have also been parallelised. One of these operations is the solution of Lyapunov equations in standard form. Parallel routines for solving these equations have been developed. These routines solve the equation obtaining directly the Cholesky factor of the solution, which fits better their application in model reduction. For this, Hammarling's method has been parallelised. The new routines solve in parallel and for dense matrices the four possible variants of standard Lyapunov equations: discrete and continuous versions, both transposed and not transposed. Interfaces offered by all the parallelised routines are similar to that of the existing routines in ScaLAPACK library, so they are easy to use from a user of this kind of libraries. The new routines work with the same data distribution used in this library: 2D block cyclic distribution, which allows many other distributions. Thanks to the developed work, now there are available high performance parallel routines to reduce linear control systems by using different variants of the Square-Root Balance & Truncate model reduction method: with or without balancing and with or without using the singular perturbation approximation formulas. They are parallel implementations of the same algorithms and methods used in the sequential