Immersion and invariance observers with time-delayed output measurements

Murguía, CG Carlos; Fey, Rhb Rob; Nijmeijer, Henk

doi:10.1016/j.cnsns.2015.06.005

Cited by 10 publications

(5 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since, these allow to rewrite exactly or approximately a complex system in a more accessible system to study. Techniques such as sector nonlinearity [147], tangent linearization [148], feedback linearization approach (Lie derivative) [149,150], passification [151][152][153][154], backstepping [155][156][157][158], immersion and invariance [159][160][161][162], and differential flatness [163][164][165], among others. On the contrary, in some cases, a linearization is proposed around an operating point.…”

Section: Stability Of Time-delaymentioning

confidence: 99%

A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

et al. 2020

View full text Add to dashboard Cite

This paper presents a brief review on the current applications and perspectives on the stability of complex dynamical systems, with an emphasis on three main classes of systems such as delay-free systems, time-delay systems, and systems with uncertainties in its parameters, which lead to some criteria with necessary and/or sufficient conditions to determine stability and/or stabilization in the domains of frequency and time. Besides, criteria on robust stability and stability of nonlinear time-delay systems are presented, including some numerical approaches.

show abstract

Section: Stability Of Time-delaymentioning

confidence: 99%

A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

et al. 2020

View full text Add to dashboard Cite

show abstract

“…The generality of the I&I formulation of the observer design problem, in connection with the Luenberger‐type observers, is shown by Ortega and Zhang 15 . I&I observers have been proposed and studied for a wide variety of applications such as Euler–Lagrange systems, 13,16 nonholonomic mechanical systems, 17 nonlinear vibrating systems, 18 attitude‐heading reference systems, 19 and systems with time‐delayed measurements 20 …”

Section: Introductionmentioning

confidence: 99%

“…15 I&I observers have been proposed and studied for a wide variety of applications such as Euler-Lagrange systems, 13,16 nonholonomic mechanical systems, 17 nonlinear vibrating systems, 18 attitude-heading reference systems, 19 and systems with time-delayed measurements. 20 The main contribution of this article is to present a geometric framework for the ESO design. We consider uncertain nonlinear systems admitting the lower-triangular form.…”

Section: Introductionmentioning

confidence: 99%

Immersion and invariance‐based extended state observer design for a class of nonlinear systems

Hosseini-Pishrobat

Keighobadi

Pirastehzad

et al. 2021

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

This article presents a novel geometric framework for the design of extended state observers (ESOs) using the immersion and invariance (I&I) method. The ESO design problem of a class of uncertain lower‐triangular nonlinear systems is considered for joint state and total disturbance observation. This problem is formulated as designing a dynamical system, as the observer, along with an appropriately defined manifold in the system‐observer extended state‐space. The ESO convergence translates into the attractivity of this manifold; that is, the convergence of the system‐observer trajectories to a small boundary layer around the manifold. The design of both reduced‐order and full‐order ESOs is studied using the I&I formulation. Moreover, an optimization method based on linear matrix inequalities is proposed to establish the convergence of ESOs. It is shown that the I&I‐based method leads to a unifying framework for the design and analysis of ESOs with linear, nonlinear, and time‐varying gains. Detailed simulations are provided to show the efficacy of the proposed ESOs.

show abstract

“…Observers designed for nonlinear systems satisfying Lipschitz condition can be classified in the aforementioned first class. Among these observers are Thau's observer [9], Linear Matrix Inequalities (LMI)-based observer [10], H ∞ -based observer [11], Geometric observer [12]- [15], observers based on sliding mode approach and its variants [16]- [19], and High Gain (HG) observer [20]- [23]. The main disadvantage of the observers belonging to this class is that they are not applicable for all nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

A New Observer for Nonlinear Systems With Application to Power Systems

Hassan

Hammuda

2019

IEEE Access

View full text Add to dashboard Cite

In this paper, a new observer is presented for discrete-time nonlinear dynamical systems. The designed observer is a modified version of the recently developed regularized least square (RLS) observer. It leads to an estimator with almost zero or very small overshoot while keeping the settling time of the estimation error very short, a case which cannot be satisfied by the well-known observers available in the literature. The predicted estimate of the developed estimator is calculated from a weighted average of a set of predicted estimate of a set of points to be generated around the filtered estimate of the state vector at a given sampling instant of time. Through this approach, we get a highly accurate result of the predicted state vector, which intuitively leads to highly accurate filtered estimates of the states. The developed estimator can deal with highly nonlinear systems, does not need any state transformation, has no restrictions on the output measurement model, leads to a unique solution, and last but not least avoids the computation of the Jacobian matrices. The convergence of the proposed observer is analyzed, and the results show its superior performance when compared with the RLS observer. Moreover, a modified version of the developed observer is proposed to reduce the computational time while maintaining its main features. Illustrative examples of highly nonlinear power systems are presented to show the effectiveness of the proposed approach and its superiority when compared with other well-known observers.INDEX TERMS Discrete-time nonlinear systems, state estimation, stability analysis, power systems.

show abstract

Immersion and invariance observers with time-delayed output measurements

Cited by 10 publications

References 15 publications

A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

Immersion and invariance‐based extended state observer design for a class of nonlinear systems

A New Observer for Nonlinear Systems With Application to Power Systems

Contact Info

Product

Resources

About