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

Juan G Rueda-Escobedo (1) , Rosane Ushirobira (2) , Denis Efimov (2) , Jaime A. Moreno (1)

1 UNAM - Universidad Nacional Autónoma de México = National Autonomous University of Mexico
2 VALSE - Finite-time control and estimation for distributed systems

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.

Mots clés: Linear Time-varying Systems; Observer; Delayed output

Domaines: Automatique / Robotique

Juan G Rueda-Escobedo, Rosane Ushirobira, Denis Efimov, Jaime A. Moreno. Gramian-based uniform convergent observer for stable LTV systems with delayed measurements. International Journal of Control, 2019, ⟨10.1080/00207179.2019.1569256⟩. ⟨hal-01889193v2⟩