All controllers for the general H control problem: LMI existence conditions and state space formulas Academic Article uri icon


  • This paper presents all controllers for the general H control problem (with no assumptions on the plant matrices). Necessary and sufficient conditions for the existence of an H controller of any order are given in terms of three Linear Matrix Inequalities (LMIs). Our existence conditions are equivalent to Scherer's results, but with a more elementary derivation. Furthermore, we provide the set of all H controllers explicitly parametrized in the state space using the positive definite solutions to the LMIs. Even under standard assumptions (full rank, etc.), our controller parametrization has an advantage over the Q-parametrization. The freedom Q (a real-rational stable transfer matrix with the H norm bounded above by a specified number) is replaced by a constant matrix L of fixed dimension with a norm bound, and the solutions (X, Y) to the LMIs. The inequality formulation converts the existence conditions to a convex feasibility problem, and also the free matrix L and the pair (X, Y) define a finite dimensional design space, as opposed to the infinite dimensional space associated with the Q-parametrization. 1994.

published proceedings

  • Automatica

author list (cited authors)

  • Iwasaki, T., & Skelton, R. E.

citation count

  • 970

complete list of authors

  • Iwasaki, T||Skelton, RE

publication date

  • August 1994