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Stabilizing Solution for a Discrete-Time Modified Algebraic Riccati Equation in Infinite Dimensions
Author
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-06-16
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We provide necessary and sufficient conditions for the existence of stabilizing solutions for a class of modified algebraic discrete-time Riccati equations (MAREs) defined on ordered Banach spaces of sequences of linear and bounded operators.
These MAREs arise in the study of linear quadratic (LQ) optimal control problems for infinite-dimensional discrete-time linear systems (DTLSs) affected simultaneously by multiplicative white noise (MN) and Markovian jumps (MJs).
Unlike most of the previous works, where the detectability and observability notions are key tools for studying the global solvability of MAREs, in this paper the conditions of existence of mean-square stabilizing solutions are given directly in terms of system parameters.
The methods we have used are based on the spectral theory of positive operators and the properties of trace class and compact operators.
Our results generalise similar ones obtained for finite-dimensional MAREs associated with stochastic DTLSs without MJs.
Also they complete and extend (in the autonomous case) former investigations concerning the existence of certain global solutions (as minimal, maximal, and stabilizing solutions) for generalized discrete-time Riccati type equations defined on infinite-dimensional ordered Banach spaces.
American Psychological Association (APA)
Ungureanu, Viorica Mariela. 2015. Stabilizing Solution for a Discrete-Time Modified Algebraic Riccati Equation in Infinite Dimensions. Discrete Dynamics in Nature and Society،Vol. 2015, no. 2015, pp.1-11.
https://search.emarefa.net/detail/BIM-1060451
Modern Language Association (MLA)
Ungureanu, Viorica Mariela. Stabilizing Solution for a Discrete-Time Modified Algebraic Riccati Equation in Infinite Dimensions. Discrete Dynamics in Nature and Society No. 2015 (2015), pp.1-11.
https://search.emarefa.net/detail/BIM-1060451
American Medical Association (AMA)
Ungureanu, Viorica Mariela. Stabilizing Solution for a Discrete-Time Modified Algebraic Riccati Equation in Infinite Dimensions. Discrete Dynamics in Nature and Society. 2015. Vol. 2015, no. 2015, pp.1-11.
https://search.emarefa.net/detail/BIM-1060451
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1060451