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access icon free A novel set-membership control strategy for discrete-time linear time-varying systems

  • Author(s): Yilian Zhang 1 ; Fuwen Yang 2 ; Qing-Long Han 3 ; Yanfei Zhu 4
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  • Source: Volume 13, Issue 18, 17 December 2019, p. 3087 – 3095
    DOI:  10.1049/iet-cta.2018.5783 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 23/07/2018, Accepted 02/09/2019, Revised 05/07/2019, Published 03/09/2019

A novel set-membership control strategy is investigated for a class of discrete time-varying systems with unknown-but-bounded noises. Different from some existing set-membership estimation based control methods, the proposed control strategy is designed by using state estimation sets instead of some specific estimation points. The controlled performance requirement is modelled as a new set-membership performance constraint which ensures that the controlled output meets the requirement at any time instant. First, the set-membership filtering method is used for obtaining the ellipsoidal state estimation set. Second, a set-membership controller is constructed by utilising the state estimation which is arbitrarily chosen from the corresponding estimation set. Accordingly, sufficient conditions are derived such that the controlled system is asymptotically stable and satisfies the proposed performance constraint in the presence of unknown-but-bounded noises at each time instant. Then, a constructive computational algorithm is provided to describe the proposed control strategy. Finally, illustrative simulation examples are presented to demonstrate the effectiveness of the proposed method.

Inspec keywords: set theory; time-varying systems; linear systems; state estimation; discrete time systems; control system synthesis; filtering theory

Other keywords: controlled system; set-membership controller; specific estimation points; corresponding estimation; unknown-but-bounded noises; controlled performance requirement; set-membership performance constraint; ellipsoidal state estimation set; existing set-membership estimation; discrete time-varying systems; set-membership filtering method; discrete-time linear time-varying systems; state estimation sets; set-membership control strategy; controlled output

Subjects: Control system analysis and synthesis methods; Time-varying control systems; Simulation, modelling and identification; Discrete control systems; Algebra; Filtering methods in signal processing; Linear control systems; Combinatorial mathematics; Other topics in statistics

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