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## A Finite Step Projective Algorithm for Solving Linear Matrix Inequalities

### Description

This paper presents an algorithm for finding feasible solutions of linear matrix inequalities. The algorithm is based on the method of alternating projections (MAP), a classical method for solving convex feasibility problems. Unlike MAP, which is an iterative method that converges asymptotically to a feasible point, the algorithm converges after a finite number of steps. The key computational component of the algorithm is an eigenvalue-eigenvector decomposition which is carried out at each...[Show more]

dc.contributor.author Orsi, Robert Rami, Mustapha Moore, John Maui USA 2015-12-13T23:09:43Z December 9 2003 078037925X http://hdl.handle.net/1885/87128 This paper presents an algorithm for finding feasible solutions of linear matrix inequalities. The algorithm is based on the method of alternating projections (MAP), a classical method for solving convex feasibility problems. Unlike MAP, which is an iterative method that converges asymptotically to a feasible point, the algorithm converges after a finite number of steps. The key computational component of the algorithm is an eigenvalue-eigenvector decomposition which is carried out at each iteration. Computational results for the algorithm are presented and comparisons are made with existing algorithms. Institute of Electrical and Electronics Engineers (IEEE Inc) IEEE Conference on Decision and Control 2003 Proceedings of the 42nd IEEE Conference on Decision and Control Keywords: Algorithms; Constraint theory; Eigenvalues and eigenfunctions; Linear systems; Mathematical models; Matrix algebra; Problem solving; Vectors; Finite step projective algorithm; Linear matrix inequalities; Control system analysis A Finite Step Projective Algorithm for Solving Linear Matrix Inequalities Conference paper Imported from ARIES Yes 2003 010203 - Calculus of Variations, Systems Theory and Control Theory MigratedxPub16281 Published Version Orsi, Robert, National ICT Australia Rami, Mustapha, University of Wurzburg Moore, John, College of Engineering and Computer Science, ANU 2037-12-31 4979 4984 2015-12-12T08:20:26Z 2-s2.0-1542289984 ANU Research Publications