High-gain interval observer for partially linear systems with bounded disturbances

Abstract

In this paper, a high-gain interval observer is proposed for a class of partially linear systems affected by unknown but bounded additive disturbances term and measurements noise. The proposed observer is based upon a classical high-gain structure from which an interval observer for the system is designed. The proposed interval observer is designed based on suitable change of coordinates which ensure the cooperativity of the system. To prove the effectiveness of the proposed approach, two numerical examples are provided and the corresponding simulation results are presented.

High-gain interval observer for continuous–discrete-time systems using an LMI design approach

“…Unfortunately, this property is hard to be satisfied in many cases. To overcome this difficulty, a time-varying change of coordinates, which is based upon the diagonalising of the observer state matrix (A − θ −1 θ KC = ν −1 diag(ρ + iω)ν) and depends on the parameter θ , has been proposed in Thabet et al (2021). In this last work, where the measurements are considered known at each instant t, the parameter θ has been arbitrarily selected and the gain K has been arbitrarily chosen such that the matrix (A − θ −1 θ KC) is C-diagonalisable and Hurwitz stable, which is not always obvious to be satisfied.…”

“…In this last work, where the measurements are considered known at each instant t, the parameter θ has been arbitrarily selected and the gain K has been arbitrarily chosen such that the matrix (A − θ −1 θ KC) is C-diagonalisable and Hurwitz stable, which is not always obvious to be satisfied. Furthermore, the selection of K becomes more and more difficult since the sufficient condition, given by Proposition 4.2 in Thabet et al (2021) and which should be verified to ensure the stability of the radius dynamic of the proposed HGIO, depends on this gain K.…”

“…These observers are designed to satisfy the cooperativity condition that guarantees that just propagating the extreme values of uncertainty intervals is enough to produce the interval bounding the set of estimated states (Efimov & Raïssi, 2016). In Thabet et al (2021), a high-gain interval observer (HGIO) is proposed for a class of partially linear systems affected by unknown but bounded additive disturbance terms and measurement noise. The proposed observer was designed based on a change of coordinates which ensures the cooperativity of the system and that the state matrix is Hurwitz stable and C-diagonalisable under some assumptions.…”

Interval observer‐based fault tolerant control strategy with fault estimation and compensation

“…The interval observer is a relatively new theory proposed by Gouzé et al [20]. It has also received great attention from many scholars in recent years [21–27]. In the present paper, we dedicate to develop an AFTC by designing an H ∞ robust controller together with a compensation controller based on fault detector and fault estimator which are both designed based on two different interval observers.…”

Finite‐time functional interval observer for linear systems with uncertainties

“…For the simplified design, the reduced order and functional IOs are, respectively, considered for linear discrete [15] and continuous‐time systems [16–18]. As the complexity of the system under observation increases, the IO has been further developed in complex systems with not only unknown uncertainty but also complicated characteristics, such as switched [19], singular [20, 21], partially linear [22], or fuzzy systems [23].…”