The Riccati Equation

Die 11 Kapitel dieses Buches geben einen Überblick über wesentliche Konzepte und Ergebnisse im Zusammenhang mit der Matrix-Riccati-Gleichung in zeitkontinuierlicher und zeitdiskreter Darstellung. Theorie, Anwendungen und numerische Algorithmen werden ausführlich behandelt. Das Vorwort gibt eine knappe Darstellung der Geschichte und Vorgeschichte der Riccati-Gleichung.

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.

Contenu
1 Count Riccati and the Early Days of the Riccati Equation.- 2 Solutions of the Continuous and Discrete Time Algebraic Riccati Equations: A Review.- 3 Algebraic Riccati Equation: Hermitian and Definite Solutions.- 4 A Geometric View of the Matrix Riccati Equation.- 5 The Geometry of the Matrix Riccati Equation and Associated Eigenvalue Methods.- 6 The Periodic Riccati Equation.- 7 Invariant Subspace Methods for the Numerical Solution of Riccati Equations.- 8 The Dissipation Inequality and the Algebraic Riccati Equation.- 9 The Infinite Horizon and the Receding Horizon LQ-Problems with Partial Stabilization Constraints.- 10 Riccati Difference and Differential Equations: Convergence, Monotonicity and Stability.- 11 Generalized Riccati Equation in Dynamic Games.