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# Bezout Factors and $\Lu$-Optimal Controllers for Delay Systems using a two-parameter Compensator Scheme

Abstract : We consider in this paper the simultaneous problem of optimal robust stabilization and optimal tracking for SISO systems in an $L^\infty$-setting using a two-parameter compensator scheme. Optimal robustness is linked to the work done by Georgiou and Smith in the $L^2$-setting. Optimal tracking involves the resolution of $L^1$-optimization problems. We consider in particular the robust control of delay systems. We determine explicit expressions of the Bezout factors for general delay systems which are in the Callier-Desoer class $\hat{\cal B}(0)$. Finally, we solve several general $L^1$-optimization problems and give an algorithm to solve the optimal robust control problem for a large class of delay systems.
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https://hal.inria.fr/inria-00073670
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Submitted on : Wednesday, May 24, 2006 - 1:27:20 PM
Last modification on : Friday, February 4, 2022 - 3:09:41 AM
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### Identifiers

• HAL Id : inria-00073670, version 1

### Citation

Catherine Bonnet, Jonathan R. Partington. Bezout Factors and $\Lu$-Optimal Controllers for Delay Systems using a two-parameter Compensator Scheme. [Research Report] RR-3023, INRIA. 1996. ⟨inria-00073670⟩

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