$H_infty$Design With First-Order Controllers Academic Article uri icon


  • The problem of determining all first order controllers (C(s)=(x1s+x2/s+x3)) which stabilize a given single-input-single-output (SISO) linear time-invariant (LTI) plant of arbitrary order has been recently solved. In this note, these results are extended to determine the subset of controllers which also satisfy various robustness and performance specifications which can be formulated as specific H norm constraints. The problem is solved by converting the H problem into the simultaneous stabilization of the closed-loop characteristic polynomial and a family of related complex polynomials. The stability boundary of each of these polynomials can be computed explicitly for fixed x3 by solving linear equations. The union of the resulting stability regions yields the set of all x1 and x2 which simultaneously satisfy the H condition and closed-loop stability for a fixed x3. The entire three- dimensional set meeting specifications is obtained by sweeping x3 over the stabilizing range. 2006 IEEE.

published proceedings

  • IEEE Transactions on Automatic Control

author list (cited authors)

  • Tantaris, R. N., Keel, L. H., & Bhattacharyya, S. P.

citation count

  • 18

complete list of authors

  • Tantaris, RN||Keel, LH||Bhattacharyya, SP

publication date

  • August 2006