In engineering theory for stability analysis Continuous Algebraic Lyapunov Equation (CALE) is an important one. In this dissertation we extend the set of Hurwitz matrix with a viable tool Singular Value Decomposition (SVD) to determine the upper solution bounds for CALE which are widely applicable methods of linear algebra,specially in stability theory.Mainly,it is a review work on "New Upper Bounds for the CALE : A Singular Value Decomposition Approach" by Svetoslav G. Savoy and Ivan P. Popchev to know more about singular value decomposition and its approaches for CALE. Among so many matrix decompositions, SVD is a reliable and widely used computational technique .In theory for practical purposes one can estimate a stability margin by using some available control bounds. But these upper bounds for CALE are valid under some restrictive condition which are inapplicable. To make them applicable this thesis is an attempt to extend the solutions of upper bounds illustrated with some numerical examples.

TITLE - A GENERAL REVIEW OF SINGULAR VALUE DECOMPOSITION (SVD) AND ITS APPROACHES FOR CONTINUOUS ALGEBRAIC LYAPUNOV EQUATION(CALE)
AUTHOR - Farhana Akter
••••••IJSER Edition - January 2014

UNIVERSITY - University of Chittagong
GUIDE NAME -
Prof. Dr. Ganesh Chandra Ray