Title :
Efficient solution of linear matrix inequalities for integral quadratic constraints
Author :
Hansson, Anders ; Vandenberghe, Lieven
Author_Institution :
Dept. of Signals, Sensors & Syst., R. Inst. of Technol., Stockholm, Sweden
Abstract :
Discusses how to implement an efficient interior-point algorithm for the semi-definite programs that result from integral quadratic constraints. The algorithm is a primal-dual potential reduction method, and the computational effort is dominated by a least-squares system that has to be solved in each iteration. The key to an efficient implementation is to utilize iterative methods and the specific structure of integral quadratic constraints. The algorithm has been implemented in Matlab. To give a rough idea of the efficiencies obtained, it is possible to solve problems resulting in a linear matrix inequality of dimension 130×130 with approximately 5000 variables in about 10 minutes on a lap-top. Problems with approximately 20000 variable and a linear matrix inequality of dimension 230×230 are solved in a few hours. It is not assumed that the system matrix has no eigenvalues on the imaginary axis, nor is it assumed that it is Hurwitz
Keywords :
iterative methods; mathematical programming; mathematics computing; matrix algebra; minimisation; Matlab; integral quadratic constraints; interior-point algorithm; least-squares system; linear matrix inequalities; primal-dual potential reduction method; semi-definite programs; Approximation algorithms; Approximation methods; Control nonlinearities; Eigenvalues and eigenfunctions; Iterative algorithms; Iterative methods; Linear matrix inequalities; Robust control; Sensor systems; USA Councils;
Conference_Titel :
Decision and Control, 2000. Proceedings of the 39th IEEE Conference on
Conference_Location :
Sydney, NSW
Print_ISBN :
0-7803-6638-7
DOI :
10.1109/CDC.2001.914735