SISO controller design to minimize a positive combination of the l1 and the ℋ2 norms

Murti V. Salapaka, Petros Voulgaris, Mohammed Dahleh

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5 Scopus citations


We consider the problem of minimizing a given positive linear combination of the l1 norm and the square of the ℋ2 norm of the closed loop over all internally stabilizing controllers. The problem is analysed for the discrete-time, SISO, linear time-invariant case. It is shown that a unique optimal solution always exists, and can be obtained by solving a finite-dimensional convex optimization problem with an a priori determined dimension. It is also established that the solution is continuous with respect to changes in the coefficients of the linear combination.

Original languageEnglish (US)
Pages (from-to)387-391
Number of pages5
Issue number3
StatePublished - Mar 1997

Bibliographical note

Funding Information:
Acknowledgements-Thisr esearch was supported by the National Science Foundation under Grants ECS-9204309, ECU216690 and ECS-9308481.

Copyright 2017 Elsevier B.V., All rights reserved.


  • Duality theory
  • Robust control


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