Controller design to optimize a composite performance measure

M. V. Salapaka, P. G. Voulgaris, M. Dahleh

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


This paper studies a mixed objective problem of minimizing a composite measure of the l1, ℋ2, and l-norms together with the l-norm of the step response of the closed loop. This performance index can be used to generate Pareto-optimal solutions with respect to the individual measures. The problem is analyzed for discrete-time, single-input single-output (SISO), linear time-invariant systems. It is shown via Lagrange duality theory that the problem can be reduced to a convex optimization problem with a priori known dimension. In addition, continuity of the unique optimal solution with respect to changes in the coefficients of the linear combination that defines the performance measure is established.

Original languageEnglish (US)
Pages (from-to)91-113
Number of pages23
JournalJournal of Optimization Theory and Applications
Issue number1
StatePublished - Oct 1996


  • Duality theory
  • Multiobjective control
  • l-optimization


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