Ebook: Matrix Riccati Equations in Control and Systems Theory
- Tags: Systems Theory Control, Operator Theory, Ordinary Differential Equations, Game Theory Economics Social and Behav. Sciences
- Series: Systems & Control: Foundations & Applications
- Year: 2003
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
The aim of the book is to present the state of the art of the theory of symmetric (Hermitian) matrix Riccati equations and to 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 is intended to make 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.
Content:
Front Matter....Pages i-xx
Basic results for linear equations....Pages 1-20
Hamiltonian Matrices and Algebraic Riccati equations....Pages 21-87
Global aspects of Riccati differential and difference equations....Pages 89-179
Hermitian Riccati differential equations....Pages 181-255
The periodic Riccati equation....Pages 257-297
Coupled and generalized Riccati Equations....Pages 299-410
Symmetric differential Riccati equations: an operator based approach....Pages 411-466
Applications to Robust Control....Pages 467-493
Non-symmetric Riccati theory and applications....Pages 495-525
Back Matter....Pages 527-572
Content:
Front Matter....Pages i-xx
Basic results for linear equations....Pages 1-20
Hamiltonian Matrices and Algebraic Riccati equations....Pages 21-87
Global aspects of Riccati differential and difference equations....Pages 89-179
Hermitian Riccati differential equations....Pages 181-255
The periodic Riccati equation....Pages 257-297
Coupled and generalized Riccati Equations....Pages 299-410
Symmetric differential Riccati equations: an operator based approach....Pages 411-466
Applications to Robust Control....Pages 467-493
Non-symmetric Riccati theory and applications....Pages 495-525
Back Matter....Pages 527-572
....