The Riccati equation
type: Item
instance of: scholarly article
title: The Riccati equation
zbMATH Open document ID: 0734.34004
published in: Communications and Control Engineering
publication date: 1992-09-18T00:00:00Z
review text: From June 26-28, 1989, a `Workshop on the Riccati equation in control, systems, and signals' was held in Como, Italy. The proceedings of the workshop have already appeared elsewhere [\textit{S. Bittani} (ed.), Proc. Workshop on the Riccati equation in control, systems, and signals, Como, Italy. Pitagora Editrice Bologna (1989)], but independently the workshop ``constituted the foundation from which the idea of this book germinated. It presents a self-contained treatment of the main issues evolving around the Riccati equation, in particular theory, applications, and numerical algorithms''. The book consists of 11 coordinated tutorial chapters written by different authors; it is intended as a graduate text as well as a reference for scientists, especially engineers, and mathematicians. The organization is as follows: Chapter 1 (\textit{S. Bittani}, Count Riccati and the early days of the Riccati equation, pp. 1-10) is devoted to the history and pre-history of the Riccati equation. Chapter 2 (\textit{P. Lancaster} and \textit{L. Rodman}, Solutions of the continuous and discrete time algebraic Riccati equations: A review, pp. 11-51) and Chapter 3 (\textit{V. Kučera}, Algebraic Riccati equations: Hermitian and definite solutions, pp. 53-88) supply a comprehensive view of the algebraic Riccati equation, mainly based on a linear algebra approach. A geometrical analysis of the equation is carried out in Chapter 4 (\textit{A. Shayman}, A geometric view of the matrix Riccati equation, pp. 89-112) and Chapter 5 (\textit{C. Martin} and \textit{G. Ammar}, The geometry of the matrix Riccati equation and associated eigenvalue methods, pp. 113-126). Chapters 2 to 5 deal with the constant coefficient case. The periodically time-varying Riccati equation is the subject of Chapter 6 (\textit{S. Bittani}, \textit{P. Colerani} and \textit{G. de Nicolao}, The periodic Riccati equation, pp. 127-162). The leading numerical techniques for the solution of the Riccati equation are overviewed i…
Mathematics Subject Classification ID: 34-02
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34A26
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 91A23
Mathematics Subject Classification ID: 00B15
Mathematics Subject Classification ID: 01A50
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93D10
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 51782
zbMATH Keywords: Riccati equation
zbMATH Keywords: Control
zbMATH Keywords: Systems
zbMATH Keywords: Signals
zbMATH Keywords: Proceedings
zbMATH Keywords: Workshop
zbMATH Keywords: Como (Italy)
zbMATH Keywords: control
zbMATH Keywords: systems
zbMATH Keywords: signals
zbMATH Keywords: history
zbMATH Keywords: algebraic Riccati equations
zbMATH Keywords: review
zbMATH Keywords: linear algebra
zbMATH Keywords: geometrical analysis
zbMATH Keywords: matrix Riccati equation
zbMATH Keywords: eigenvalue methods
zbMATH Keywords: numerical techniques
zbMATH Keywords: Invariant subspace methods
zbMATH Keywords: dissipation inequality
zbMATH Keywords: dissipative systems
zbMATH Keywords: linear-quadratic optimal control
zbMATH Keywords: stability theory for feedback control systems
zbMATH Keywords: electrical network synthesis
zbMATH Keywords: covariance generation
zbMATH Keywords: \(H_{\infty }\) control problem
zbMATH Keywords: dynamic games
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 51782