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 nonlinearities 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.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Juan G. Rueda-Escobedo http://orcid.org/0000-0001-5747-060X
Denis Efimov http://orcid.org/0000-0001-8847-5235
Jaime A. Moreno http://orcid.org/0000-0002-2556-9784
Notes
1 For ,
is a strict positive monotonic function of v, then its image is
.