Observability through delayed measurements: a new approach to state observers design

Abstract

An original approach for the construction of state observers for dynamic systems is presented in this article. New notions of observability (delay-observability and delay-drift-observability), useful for the development of the observer equations and for the convergence proof, are introduced and compared with other standard observability concepts. In particular, it is shown that delay-drift-observability is an extension of the well-known drift-observability property. The construction of the proposed observer is straightforward and does not require any coordinate transformation of the system into a canonical form, which is a common feature of many other approaches. A numerical example is reported, where a system that is not drift-observable is considered. In this case, the proposed observer is easily constructed and performs well.

Modulating function‐based fast convergent observer and output feedback control for a class of non‐linear systems

“…The concept of drift‐observability is introduced in [54, 55]. This concept means that the state can be reconstructed on the basis of knowledge of the output and its first derivatives [54–56]. Definition 1 System (1) is said to be drift‐observable in if the map where is a diffeomorphism in [54].…”

High gain observer design for fractional‐order non‐linear systems with delayed measurements: application to synchronisation of fractional‐order chaotic systems

“…Each observer estimates delayed states at each delayed time instant. This idea has been extended with further developments in [46–48].…”