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Gramian-based uniform convergent observer for stable LTV systems with delayed measurements

Juan Rueda-Escobedo 1 Rosane Ushirobira 2 Denis Efimov 2 Jaime Moreno 1
2 VALSE - Finite-time control and estimation for distributed systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : In this work, an observer for a linear time-varying system with delayed measurements is developed. The delay is assumed to be unknown, bounded, and it can be time-varying with no restriction on its rate of change. The observer uses auxiliary signals related to the constructibility Gramian of the system and it contains nonlin-earities that provide a uniform fixed-time convergence to a bounded region in the estimation error coordinates. This means that the convergence time can be bounded by a positive constant which is independent from the initial conditions and the initial time. This property is new for the addressed class of systems. The ultimate bound of the estimation error depends on the maximum difference between the nominal output and the delayed one, and not directly on the delay size or its time derivative. These properties are illustrated in a numerical simulation.
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https://hal.inria.fr/hal-01889193
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Submitted on : Thursday, October 10, 2019 - 10:59:10 AM
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Juan Rueda-Escobedo, Rosane Ushirobira, Denis Efimov, Jaime Moreno. Gramian-based uniform convergent observer for stable LTV systems with delayed measurements. International Journal of Control, Taylor & Francis, 2019, ⟨10.1080/00207179.2019.1569256⟩. ⟨hal-01889193v2⟩

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