Matrix Riccati Equations in Control and Systems Theory
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 differe...
| Main Authors: | , , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser
2003, 2003
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| Edition: | 1st ed. 2003 |
| Series: | Systems & Control: Foundations & Applications
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Basic results for linear equations
- 1.1 Linear differential equations and linear algebraic equations
- 1.2 Exponential dichotomy and L2evolutions
- 2 Hamiltonian Matrices and Algebraic Riccati equations
- 2.1 Solutions of algebraic Riccati equations and graph subspaces
- 2.2 Indefinite scalar products and a canonical form of Hamiltonian matrices
- 2.3 Hermitian algebraic Riccati equations
- 2.4 Positive semi-definite solutions of standard algebraic Riccati equations
- 2.5 Hermitian discrete-time algebraic Riccati equations
- 3 Global aspects of Riccati differential and difference equations
- 3.1 Riccati differential equations and associated linear systems
- 3.2 A representation formula
- 3.3 Flows on Graßmann manifolds: The extended Riccati differential equation
- 3.4 General representation formulae for solutions of RDE and PRDE, the time-continuous and periodic Riccati differential equation, and dichotomy
- 9.1 Non-symmetric Riccati theory
- 9.2 Application to open loop Nash games
- 9.3 Application to open loop Stackelberg games
- A Appendix
- A.1 Basic facts from control theory
- A.2 The implicit function theorem
- References
- List of Figures
- 6.4 Non-symmetric Riccati equations in open loop Stackelberg differential games
- 6.5 Discrete-time open loop Stackelberg equations
- 6.6 Coupled Riccati equations in closed loop Nash differential games
- 6.7 Rational matrix differential equations arising in stochastic control
- 6.8 Rational matrix difference equations arising in stochastic control
- 6.9 Coupled Riccati equations in Markovian jump systems
- 7 Symmetric differential Riccati equations: an operator based approach
- 7.1 Popov triplets: definition and equivalence
- 7.2 Associated objects
- 7.3 Associated operators
- 7.4 Existence of the stabilizing solution
- 7.5 Positivity theory and applications
- 7.6 Differential Riccati inequalities
- 7.7 The signature condition
- 7.8 Differential Riccati theory: A Hamiltonian descriptor operator approach
- 8 Applications to Robust Control Systems
- 8.1 The Four Block Nehari Problem
- 8.2 Disturbance Attenuation
- 9 Non-symmetric Riccati theory and applications
- 3.5 A representation formula for solutions of the discrete time Riccati equation
- 3.6 Global existence results
- 4 Hermitian Riccati differential equations
- 4.1 Comparison results for HRDE
- 4.2 Monotonicity and convexity results: A Fréchet derivative based approach
- 4.3 Convergence to the semi-stabilizing solution
- 4.4 Dependence of HRDE on a parameter
- 4.5 An existence theorem for general HRDE
- 4.6 A special property of HRDE
- 5 The periodic Riccati equation
- 5.1 Linear periodic differential equations
- 5.2 Preliminary notation and results for linear periodic systems
- 5.3 Existence results for periodic Hermitian Riccati equations
- 5.4 Positive semi-definite periodic equilibria of PRDE
- 6 Coupled and generalized Riccati equations
- 6.1 Some basic concepts in dynamic games
- 6.2 Non-symmetric Riccati equations in open loop Nash differential games.-6.3 Discrete-time open loop Nash Riccati equations