Orsi, RobertRami, MustaphaMoore, John2015-12-13December 9078037925Xhttp://hdl.handle.net/1885/87128This 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.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 analysis20032015-12-12