Optimal and Robust Controllers for Periodic and Multirate Systems

Munther A. Dahleh, Petros G. Voulgaris, Lena S. Valavani

Research output: Contribution to journalArticlepeer-review


In this paper, the problem of optimal rejection of bounded persistent disturbances is solved in the case of linear discrete-time periodic systems. The solution consists of solving an equivalent time-invariant standard l1 optimization problem subject to an additional constraint. This constraint assures the causality of the resulting periodic controller. By the duality theory, the problem is shown to be equivalent to a linear programming problem, which is no harder than the standard I1 problem. Also, it is shown that the method of solution presented applies exactly to the problem of disturbance rejection in the case of multirate sampled data systems. Finally, we apply the results to the problem of robust stabilization of periodic and multirate systems.

Original languageEnglish (US)
Pages (from-to)90-99
Number of pages10
JournalIEEE Transactions on Automatic Control
Issue number1
StatePublished - Jan 1992
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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