l(1)-optimality of feedback control systems - The SISO discrete-time case

Controllers that optimally reject a class of disturbances are considered. The problem of determining when a stabilizing control is l(1)-optimal for a given plant is studied for some stable weighting function. This problem belongs to the class of inverse problems in optimal control introduced by Kalm...

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Bibliographic Details
Published in:IEEE transactions on automatic control 1990-09, Vol.35, p.1082-1085
Main Authors: Deodhare, Girish, Vidyasagar, M
Format: Article
Language:English
Online Access:Get full text
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Summary:Controllers that optimally reject a class of disturbances are considered. The problem of determining when a stabilizing control is l(1)-optimal for a given plant is studied for some stable weighting function. This problem belongs to the class of inverse problems in optimal control introduced by Kalman. It is shown that, for a given plant, the set of all the H(infinity)-optimal controllers (obtained by considering all stable weighting functions with no zeros on the unit circle) is actually contained in the corresponding set of l(1)-optimal controllers. It is also demonstrated that an l(1)-optimal controller, unlike an H(infinity)-optimal controller, can remain l(1)-optimal for the same plant for a wide range of nontrivially different weighting functions. (I.E.)
ISSN:0018-9286