Mixed objective control synthesis: Optimal ℓ1/H2 control

Murti V. Salapaka, Mohammed Dahleh, Petros Voulgaris

Research output: Contribution to journalArticlepeer-review


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 analyzed for the discrete-time, single-input single-output (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. Thus, the problem can be 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)1672-1689
Number of pages18
JournalSIAM Journal on Control and Optimization
Issue number5
StatePublished - Sep 1997


  • Discrete time
  • Duality
  • Robust control
  • ℓ optimization

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


Dive into the research topics of 'Mixed objective control synthesis: Optimal ℓ1/H2 control'. Together they form a unique fingerprint.

Cite this