l1-optimality of feedback control systems: the SISO discrete-time case

Deodhare, G. ; Vidyasagar, M. (1990) l1-optimality of feedback control systems: the SISO discrete-time case IEEE Transactions on Automatic Control, 35 (9). pp. 1082-1085. ISSN 0018-9286

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Related URL: http://dx.doi.org/10.1109/9.58544


Controllers that optimally reject a class of disturbances are considered. The problem of determining when a stabilizing control is l1-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-optimal controllers (obtained by considering all stable weighting functions with no zeros on the unit circle) is actually contained in the corresponding set of l1-optimal controllers. It is also demonstrated that an l1-optimal controller, unlike an H-optimal controller, can remain l1-optimal for the same plant for a wide range of nontrivially different weighting functions.

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