Mixed objective control synthesis: optimal l1/H2 control

Murti V. Salapaka, Mohammed Dahleh, Petros Voulgaris

Research output: Contribution to journalConference articlepeer-review

14 Scopus citations


In this paper we consider the problem of minimizing the l1 norm of the transfer function from the exogenous input to the regulated output over all internally stabilizing controllers while keeping its H2 norm under a specified level. The problem is analysed for the discrete-time, SISO, linear time invariant case. It is shown that an optimal solution always exists. Duality theory is employed to show that any optimal solution is a finite impulse response sequence and an a priori bound is given on its length. The problem is reduced to a finite dimensional convex optimization problem with an a priori determined dimension. Finally it is shown that, in the region of interest of the H2 constraint level the optimal is unique and continuous with respect to changes in the constraint level.

Original languageEnglish (US)
Pages (from-to)1438-1442
Number of pages5
JournalProceedings of the American Control Conference
StatePublished - Jan 1 1995
EventProceedings of the 1995 American Control Conference. Part 1 (of 6) - Seattle, WA, USA
Duration: Jun 21 1995Jun 23 1995


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