Geodesic
$\ell^1$-optimal control for multirate systems under full state feedback
Kybernetika, Tome 35 (1999) no. 5, p. [555].

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This paper considers the minimization of the $\ell ^\infty $-induced norm of the closed loop in linear multirate systems when full state information is available for feedback. A state-space approach is taken and concepts of viability theory and controlled invariance are utilized. The essential idea is to construct a set such that the state may be confined to that set and that such a confinement guarantees that the output satisfies the desired output norm conditions. Once such a set is computed, it is shown that a memoryless nonlinear controller results, which achieves near-optimal performance. The construction involves the solution of several finite linear programs and generalizes to the multirate case earlier work on linear time-invariant (LTI) systems.
Classification : 93B36, 93B52, 93C05, 93C35
Keywords: state-space approach; full state feedback; $\ell^1$ norm; multirate system; near-optimal performance; memoryless nonlinear controller; viability theory 
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     author = {Aubrecht, Johannes and Voulgaris, Petros G.},
     title = {$\ell^1$-optimal control for multirate systems under full state feedback},
     journal = {Kybernetika},
     pages = {[555]},
     publisher = {mathdoc},
     volume = {35},
     number = {5},
     year = {1999},
     mrnumber = {1728468},
     zbl = {1274.93098},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1999__35_5_a1/}
}
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Aubrecht, Johannes; Voulgaris, Petros G. $\ell^1$-optimal control for multirate systems under full state feedback. Kybernetika, Tome 35 (1999) no. 5, p. [555]. http://geodesic.mathdoc.fr/item/KYB_1999__35_5_a1/