Proportional-delayed controllers design for LTI-systems a geometric approach

Abstract : This paper focuses on the design of P-δ controllers for single-input-single-output linear time-invariant systems. The basis of this work is a geometric approach allowing to partitioning the parameter space in regions with constant number of unstable roots. This methodology defines the hyper-planes separating the aforementioned regions and characterises the way in which the number of unstable roots changes when crossing such a hyper-plane. The main contribution of the paper is that it provides an explicit tool to find P-δ gains ensuring the stability of the closed-loop system. In addition, the proposed methodology allows to design a non-fragile controller with a desired exponential decay rate σ. Several numerical examples illustrate the results and a haptic experimental set-up shows the effectiveness of P-δ controllers. © 2017 Informa UK Limited, trading as Taylor and Francis Group.
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J.-E. Hernández-Díez, C.-F. Méndez-Barrios, S. Mondié, Silviu-Iulian Niculescu, E.J. González-Galván. Proportional-delayed controllers design for LTI-systems a geometric approach. International Journal of Control, 2018, 91 (4), pp.907-925. ⟨10.1080/00207179.2017.1299943⟩. ⟨hal-02281719⟩



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