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State-space H infini control : a complete solution via convex Riccati inequalities

Abstract : The most general H control problem is solved by elementary state-space manipulations. Here the characterization of feasible closed-loop gains g is in terms of Riccati inequalities rather than equations. This allows treatment within a single framework of both regular and singular continuous - or discrete - time H problems. An interesting by-product of this approach is a convex state-space parametrization of all H suboptimal controllers, including reduced-order ones. Here the free parameters are pairs of positive definite matrices solving the Riccati inequalities and satisfying some coupling constraint. Such pairs form a convex set and given any of them, the controller reconstruction amounts to solving a linear matrix inequality (LMI). Applications of these results to the improvement of classical H design techniques are discussed.
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https://hal.inria.fr/inria-00077034
Contributor : Rapport de Recherche Inria <>
Submitted on : Monday, May 29, 2006 - 11:56:30 AM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM
Long-term archiving on: : Friday, May 13, 2011 - 10:39:19 PM

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  • HAL Id : inria-00077034, version 1

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Pascal Gahinet, Pierre Apkarian. State-space H infini control : a complete solution via convex Riccati inequalities. [Research Report] RR-1794, INRIA. 1992. ⟨inria-00077034⟩

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