Matrix equations solutions using Riccati equation: Theory and Applications - Softcover

Nicholas Assimakis, Maria Adam And

Softcover

ISBN 10: 3659227323 ISBN 13: 9783659227325

Publisher: LAP LAMBERT Academic Publishing, 2012

Synopsis

The nonlinear matrix equation X^{s}+A*X^{-s})A=Q, when A is a square matrix, Q is a square positive definite matrix and s an integer number, has been studied by several authors. Equations of this type arise in many problems of systems theory, discrete time control and in many applications in various research areas including filter design, ladder networks, dynamic programming, stochastic filtering and statistics. In the case that A is nonsingular and s=1, the associated matrix equation has many contributions in the theory, applications and numerical solution of the discrete algebraic Riccati equation. In this book, necessary and sufficient conditions for the existence of the Hermitian solutions are presented as well as an algebraic method based on the Riccati equation for the computation of these solutions is proposed. Inequalities for the eigenvalues of A, Q are presented. Bounds for the extreme eigenvalues of the minimal solution are derived. These results are verified through numerical experiments. This book concerns graduate students as well as researchers in the fields of Applied Mathematics, Electrical and Computer Engineering.

About this title

About the Author

Maria Adam: Ph.D. in Applied Mathematics, National Technical University of Athens, 2001. Assistant Professor at University of Central Greece. Nicholas Assimakis: Ph.D. in Signal Processing, University of Patras, 1993. Associate Professor at Technological Educational Institute of Lamia, Greece.

Edition details

• Publisher: LAP LAMBERT Academic Publishing
• Publication date: 2012
• Language: English
• ISBN 10: 3659227323
• ISBN 13: 9783659227325
• Binding: Paperback
• Number of pages: 92