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Titlebook: Rational Matrix Equations in Stochastic Control; Tobias Damm Book 2004 Springer-Verlag Berlin Heidelberg 2004 Generalized Lyapunov Equatio

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发表于 2025-3-21 16:38:21 | 显示全部楼层 |阅读模式
书目名称Rational Matrix Equations in Stochastic Control
编辑Tobias Damm
视频video
概述Detailed study with survey character on rational matrix equations in stochastic control
丛书名称Lecture Notes in Control and Information Sciences
图书封面Titlebook: Rational Matrix Equations in Stochastic Control;  Tobias Damm Book 2004 Springer-Verlag Berlin Heidelberg 2004 Generalized Lyapunov Equatio
描述.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treatment of rational matrix equations in stochastic systems, including various aspects of the field, previously unpublished results and explicit examples.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..
出版日期Book 2004
关键词Generalized Lyapunov Equations; Generalized Riccati Equations; H Infinity Control; Matrix; Positive Oper
版次1
doihttps://doi.org/10.1007/b10906
isbn_softcover978-3-540-20516-6
isbn_ebook978-3-540-40001-1Series ISSN 0170-8643 Series E-ISSN 1610-7411
issn_series 0170-8643
copyrightSpringer-Verlag Berlin Heidelberg 2004
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发表于 2025-3-21 23:14:07 | 显示全部楼层
Optimal stabilization of linear stochastic systems, problems..A classical problem in optimal control theory is the so-called linear quadratic (LQ-)stabilization problem. Among all controls that stabilize a given system, one determines the one that satisfies a certain quadratic nonnegative semidefinite cost-functional. This will be the topic of the f
发表于 2025-3-22 02:35:37 | 显示全部楼层
Linear mappings on ordered vector spaces,of the type occuring e.g. in Theorem 1.5.3. It is crucial to observe that these Lyapunov operators possess certain positivity properties, which will be discussed in the following. The present chapter is split in two parts. In the first part, we introduce the general notions of ordered Banach spaces
发表于 2025-3-22 05:50:12 | 显示全部楼层
,Newton’s method,form (2.27), derived in Chapter 2, which we view, very generally, as nonlinear operator equations in an ordered vector space. A standard method to solve nonlinear equations is the Newton iteration. Its applicability to operator equations in normed spaces was first established by Kantorovich in [122]
发表于 2025-3-22 12:33:51 | 显示全部楼层
Solution of the Riccati equation,rms of rational matrix inequalities. Now we analyze these matrix inequalities and the corresponding matrix equations. To this end, we first introduce an abstract form of the Riccati operators met in the Sections 2.1 – 2.3, and the definite and the indefinite constraints mentioned in Remark 2.3.7. Re
发表于 2025-3-22 16:07:57 | 显示全部楼层
Book 2004 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 intend
发表于 2025-3-22 18:24:35 | 显示全部楼层
Optimal stabilization of linear stochastic systems,irst section..The same techniques used to find an LQ-optimal stabilization can also be applied to identify a worst-case perturbation of a control system. This leads to the Bounded Real Lemma, which is the topic of Section 2.2. The Bounded Real Lemma itself, is the main tool needed to tackle the disturbance attenuation problem in Section 2.3.
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发表于 2025-3-23 02:12:21 | 显示全部楼层
0170-8643 atrix 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..978-3-540-20516-6978-3-540-40001-1Series ISSN 0170-8643 Series E-ISSN 1610-7411
发表于 2025-3-23 05:42:25 | 显示全部楼层
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