Matrix Riccati Equations In Control And Systems Theory
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| Author | : Hisham Abou-Kandil |
| Publisher | : Birkhäuser |
| Total Pages | : 584 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3034880812 |
The authors present the theory of symmetric (Hermitian) matrix Riccati equations and contribute to the development of the theory of non-symmetric Riccati equations as well as to certain classes of coupled and generalized Riccati equations occurring in differential games and stochastic control. The volume offers a complete treatment of generalized and coupled Riccati equations. It deals with differential, discrete-time, algebraic or periodic symmetric and non-symmetric equations, with special emphasis on those equations appearing in control and systems theory. Extensions to Riccati theory allow to tackle robust control problems in a unified approach. The book makes available classical and recent results to engineers and mathematicians alike. It is accessible to graduate students in mathematics, applied mathematics, control engineering, physics or economics. Researchers working in any of the fields where Riccati equations are used can find the main results with the proper mathematical background.
| Author | : H. Abou-Kandil |
| Publisher | : Birkhauser |
| Total Pages | : 571 |
| Release | : 2003-01 |
| Genre | : Mathematics |
| ISBN | : 9780817600853 |
The volume offers a complete treatment of generalized and coupled Riccati equations. It deals with differential, discrete-time, algebraic or periodic symmetric and non-symmetric equations, with special emphasis on those equations appearing in control and systems theory. Extensions to Riccati theory allow to tackle robust control problems in a unified approach."
| Author | : Sergio Bittanti |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 346 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 3642582230 |
Conceived by Count Jacopo Francesco Riccati more than a quarter of a millennium ago, the Riccati equation has been widely studied in the subsequent centuries. Since its introduction in control theory in the sixties, the matrix Riccati equation has known an impressive range of applications, such as optimal control, H? optimization and robust stabilization, stochastic realization, synthesis of linear passive networks, to name but a few. This book consists of 11 chapters surveying the main concepts and results related to the matrix Riccati equation, both in continuous and discrete time. Theory, applications and numerical algorithms are extensively presented in an expository way. As a foreword, the history and prehistory of the Riccati equation is concisely presented.
| Author | : M.I. Zelikin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 296 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 3662041367 |
The only monograph on the topic, this book concerns geometric methods in the theory of differential equations with quadratic right-hand sides, closely related to the calculus of variations and optimal control theory. Based on the author’s lectures, the book is addressed to undergraduate and graduate students, and scientific researchers.
| Author | : Tobias Damm |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 228 |
| Release | : 2004-01-23 |
| Genre | : Mathematics |
| ISBN | : 9783540205166 |
This book is the first comprehensive treatment of rational matrix equations in stochastic systems, including various aspects of the field, previously unpublished results and explicit examples. Topics include modelling with stochastic differential equations, stochastic stability, reformulation of stochastic control problems, analysis of the rational matrix equation and numerical solutions. Primarily a survey in character, this monograph is intended for researchers, graduate students and engineers in control theory and applied linear algebra.
| Author | : Aleksandr Ivanovič Egorov |
| Publisher | : Pensoft Publishers |
| Total Pages | : 390 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 9789546422965 |
Presents the necessary auxiliary facts from algebra, functional analysis and Lie group analysis. This book illustrates theory with solutions of numerous examples. It also presents the matrix Riccati equations. It deals with theoretical questions concerning matrix and operator equations based on various applied problems from mathematical physics.
| Author | : Peter Lancaster |
| Publisher | : Clarendon Press |
| Total Pages | : 502 |
| Release | : 1995-09-07 |
| Genre | : Mathematics |
| ISBN | : 0191591254 |
This book provides a careful treatment of the theory of algebraic Riccati equations. It consists of four parts: the first part is a comprehensive account of necessary background material in matrix theory including careful accounts of recent developments involving indefinite scalar products and rational matrix functions. The second and third parts form the core of the book and concern the solutions of algebraic Riccati equations arising from continuous and discrete systems. The geometric theory and iterative analysis are both developed in detail. The last part of the book is an exciting collection of eight problem areas in which algebraic Riccati equations play a crucial role. These applications range from introductions to the classical linear quadratic regulator problems and the discrete Kalman filter to modern developments in HD*W*w control and total least squares methods.
| Author | : Zoran Gajic |
| Publisher | : Courier Corporation |
| Total Pages | : 274 |
| Release | : 2008-01-01 |
| Genre | : Mathematics |
| ISBN | : 048646668X |
This comprehensive treatment provides solutions to many engineering and mathematical problems related to the Lyapunov matrix equation, with self-contained chapters for easy reference. The authors offer a wide variety of techniques for solving and analyzing the algebraic, differential, and difference Lyapunov matrix equations of continuous-time and discrete-time systems. 1995 edition.
| Author | : Stephen Barnett |
| Publisher | : |
| Total Pages | : 216 |
| Release | : 1984 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Dario A. Bini |
| Publisher | : SIAM |
| Total Pages | : 261 |
| Release | : 2012-03-31 |
| Genre | : Mathematics |
| ISBN | : 1611972086 |
This treatment of the basic theory of algebraic Riccati equations describes the classical as well as the more advanced algorithms for their solution in a manner that is accessible to both practitioners and scholars. It is the first book in which nonsymmetric algebraic Riccati equations are treated in a clear and systematic way. Some proofs of theoretical results have been simplified and a unified notation has been adopted. Readers will find a unified discussion of doubling algorithms, which are effective in solving algebraic Riccati equations as well as a detailed description of all classical and advanced algorithms for solving algebraic Riccati equations and their MATLAB codes. This will help the reader gain an understanding of the computational issues and provide ready-to-use implementation of the different solution techniques.
