Robust synthesis in ℓ1: A globally optimal solution

Mustafa Khammash, Murti V. Salapaka, Tim Van Voorhis

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


In this paper, a method to synthesize controllers that achieve globally optimal robust performance within any prespecified tolerance, against structured norm-bounded time-varying and/or nonlinear uncertainty is developed. The performance measure considered is the infinity to infinity induced norm of a system's transfer function. The method developed utilizes linear relaxation techniques to solve the infinite dimensional nonconvex problem via finite dimensional linear programming problems.

Original languageEnglish (US)
Pages (from-to)1744-1754
Number of pages11
JournalIEEE Transactions on Automatic Control
Issue number11
StatePublished - Nov 2001
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received July 7, 2000; revised January 10, 2001 and April 8, 2001. Recommended by Associate Editor K. M. Grigoriadis. This was was supported by the National Science Foundation under Grants ECS-9733802, ECS-9110764, ECS-9457485, and by Iowa State University under Grant SPRIGS-7041747. M. Khammash and M. V. Salapaka are with the Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011 USA. T. Van Voorhis is with the Department of Industrial and Manufacturing Systems Engineering, Iowa State University, Ames, IA 50011 USA. Publisher Item Identifier S 0018-9286(01)10345-4.


  • Optimal
  • Robustness
  • Uncertainty


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