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Explicit controller formulas for LMI-based H synthesis

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1 Author(s)
Gahinet, P. ; Inst. Nat. de Recherche en Inf. et Autom., Le Chesnay, France

The set of H controllers with closed-loop performance γ can be implicitly parametrized by the solutions R, S of a system of linear matrix inequalities (LMI). The matrices R, S play a role analogous to that of the Riccati solutions X and Y in classical state-space H control. Useful applications of this parametrization include reduced-order H synthesis, mixed H2/H design, H design with a pole placement constraint, etc. This paper is concerned with the computation of H controllers given any solution (R, S) of the characteristic system of LMIs. Explicit and numerically reliable formulas are derived for both full- and reduced-order cases. Remarkably, these formulas turn out to be simple extensions of the usual "central controller" formulas where the LMI solutions R, S replace the Riccati solutions X, Y. In addition, they apply to regular as well as singular H problems. Finally, the LMI-based approach also leads to simple and numerically appealing new formulas for discrete-time H controllers.

Published in:

American Control Conference, 1994  (Volume:3 )

Date of Conference:

29 June-1 July 1994