NDLI: Realization theory and quadratic optimal controllers for systems defined over Banach and Frechét algebras

Content Provider	IEEE Xplore Digital Library
Author	Byrnes, C.I.
Copyright Year	1980
Description	Author affiliation: Harvard University, Cambridge, Mass. (Byrnes, C.I.)
Abstract	If a system (A,B,C) depends in a bounded, measurable, continuous, smooth or even analytic manner on plant parameters, then a very important and natural problem to study is the existence of a feedback law F, which is a switching gain in the sense that F depends on (A,B,C) and in this way depends on the plant parameters, which stabilizes the system for all values of the parameter and which has the same kind of dependence on the paramters. Using the Gel'fand theory for Banach algebras, the author proved such a theorem in the bounded measurable case under reasonable hypothesis deriving this case and the continuous case from the analytic case by use of the operational calculus and earlier work on systems with parameters. Now, recent work by E. Kamen on the stability of half-plane digital filters shows that similar problems for other Banach algebras also arise in applications. This situation makes the construction of a realization theory for and of stabilizability criteria for systems defined over a Banach or Frechét algebra A desirable, and in this paper we develop such a theory with special emphasis on the construction of finitely-generated realizations, the existence of coprime factorizations for T(s) defined over A, and solvability of the quadratic optimal control problem and the associated algebraic Riccati equation over A.
Starting Page	247
Ending Page	251
File Size	415243
Page Count	5
File Format	PDF
DOI	10.1109/CDC.1980.271791
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1980-12-10
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Optimal control Control systems Algebra Riccati equations Linear systems Weight control Mathematics Gain measurement Feedback Calculus
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

On Riccati Equations in Banach Algebras

Riccati Equations on Noncommutative Banach Algebras

Quadratic Optimization for Fixed Order Linear Controllers via Covariance Control

Stabilizability of linear discrete-time systems defined over a commutative normed algebra

The singular linear-quadratic regulator problem and the Goh-Riccati equation

Quadratic stabilizability and proper controllers

Feedback Solutions of Optimal Control Problems with DAE Constraints

Designing Stabilizing Controllers for Uncertain Systems using the Riccati Equation Approach

Quadratic optimal control of well-posed linear systems

Realization theory and quadratic optimal controllers for systems defined over Banach and Frechét algebras

Similar Documents

On Riccati Equations in Banach Algebras

Riccati Equations on Noncommutative Banach Algebras

Quadratic Optimization for Fixed Order Linear Controllers via Covariance Control

Stabilizability of linear discrete-time systems defined over a commutative normed algebra

The singular linear-quadratic regulator problem and the Goh-Riccati equation

Quadratic stabilizability and proper controllers

Feedback Solutions of Optimal Control Problems with DAE Constraints

Designing Stabilizing Controllers for Uncertain Systems using the Riccati Equation Approach

Quadratic optimal control of well-posed linear systems

Realization theory and quadratic optimal controllers for systems defined over Banach and Frechét algebras