On the existence of optimal stabilizing controls

Author

Jones, E.L.

Author_Institution

University of Witwatersrand, Johannesburg, South Africa

Volume

Issue

fYear

1979

fDate

2/1/1979 12:00:00 AM

Firstpage

122

Lastpage

124

Abstract

A rather general sufficient condition is given for the stability of linear systems that may be used to extend the limited state LQR problem, or Lyapunov\´s stability criterion. Note: Let $\\dot{x}= Ax + Bu + D\\upsilon$ $y=Cx$ and $J= \\int (frac{1}{2}x^{T}C^{T}_{o}x + frac{1}{2} u^{v}tRu)dt$ then $u$ is called the control $\\upsilon$ is called the influence $y$ is called the output and yois called the synthetic output where $y_{o}=C_{o}x$ . If we choose $u=Fy$ as a control we get the autonomous linear system $\\dot{x}=A(F)x + D\\upsilon$ where $A(F)=A-BFC$ . We may not choose the control to be a function of the synthetic output, nor may we in any way choose the influence.

Keywords

Linear systems, time-invariant continuous-time; Optimal regulators; Stability; Automatic control; Control systems; Equations; Feedback control; Linear feedback control systems; Linear systems; Optimal control; Regulators; Stability; Sufficient conditions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1979.1101954

Filename

1101954

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=828501