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

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.

KEYWORDS:

• Observer
• delayed output
• linear time-varying systems

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 $v\ge 0$, $k_{1}v+k_2{v}^{\frac{p+1}{2}}$ is a strict positive monotonic function of v, then its image is ${\mathbb{R}}_{\ge 0}$.

Additional information

Funding

This work is supported in part by the Institut national de recherche en informatique et en automatique HoTSMoCE Inria associate team program; Government of Russian Federation (grant 074-U01); Ministry of Education and Science of Russian Federation (project 14.Z50.31.0031); by the financial support from PAPIIT-UNAM, project IN113614; Fondo de colaboración II-FI UNAM, project IISGBAS-100-2015; Consejo Nacional de Ciencia y Tecnología (CONACyT), project 241171; and CONACyT CVU 491701.