Design and applications of interval observers for uncertain dynamical systems

In this work, vector framework based contraction theory to design interval observers for a class of nonlinear systems having disturbances, inputs and outputs is exploited. The main feature is that it does not require the formulation of error dynamics to show the convergence properties and need not require the construction of a Lyapunov candidate function without any idea of the structure of the function. Specifically, it performs the convergence analysis through a comparison system which has specified properties. Furthermore, this theory is exploited to design dynamic output feedback control through the obtained state bounds from the constructed interval observer and the system outputs, to make the interval observer to be globally asymptotically stable. Examples with simulation outcomes are provided to validate the theoretical results.

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“…Several researchers (see refs. [17–20]) proved this convergence property using Lyapunov stability analysis.…”

Section: Introductionmentioning

confidence: 93%

Interval observer design for nonlinear systems using simplified contraction theory

Singh

Xiong

Dinh

et al. 2022

IET Control Theory & Appl

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“…They are also successfully applied to solve many real-time life problems. [19][20][21][22] Exhaustive reviews can be found in References 14,23,24. It should be noted that all mentioned above papers solve the problem of full state vector interval estimation while only a specified function of the state vector may be necessary in practice. Such an approach based on functional interval observers was suggested in References 25-28 enables estimating some linear function of the state vector.…”

Section: Introductionmentioning

confidence: 99%

Interval observer design for nonlinear discrete‐time dynamic systems

Zhirabok,

Zuev,

Filaretov

2024

Adaptive Control & Signal

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SummaryThe problem of interval observer design for systems described by nonlinear models with uncertainties is considered. The problem is solved based on special mathematical technique (the algebra of functions) which allows obtaining solution for systems containing non‐smooth nonlinearities. The relations to design interval observer insensitive or having minimal sensitivity to the disturbance and estimating the prescribed nonlinear function of the state vector of the original system are derived. Theoretical results are illustrated by example.

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“…Also this model has demographic and environmental ambiguity. Khan et al [21], Mazenc and Bernard [22] and Sergiyenko et al [23] developed the design and applications of interval observers for uncertain dynamical systems . Also their approach is substantially different from traditional methods for establishing control laws for discrete and continuous time perturbed processes or performing robust stability analysis.…”

Section: Introductionmentioning

confidence: 99%

“…Tang et al [24] proposed a two step interval estimation method for discrete time linear systems by integrating robust observer design and reachability analysis. Efimov et al [21,22] studied the interval state observer design for time-varying discrete-time systems and they offered three solutions: For a generic timevarying system, a system with positive state, and a particular type of periodic systems and also they reviewed the important tools and techniques for design of interval observers for continuous-time, discrete-time and timedelayed systems. Feeney [25] explained the population dynamics based on birth intervals and parity progression.…”

Section: Introductionmentioning

confidence: 99%

Diagonal canonical form of interval matrices and applications on dynamical systems

Nirmala

Ganesan

2023

Phys. Scr.

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Finding the simplest form of a set of quantities is an important aspect of any branch of Mathematics. Of course, the simplest form or the canonical form as we often call it in mathematics, must possess all the important characteristics of the set of quantities. A real square matrix satisfying certain conditions can be brought to diagonal form which is its simplest form such that the diagonal form retains the eigenvalues, determinants, trace, rank, nullity,.. of the original matrix.Many computations with matrices become easier if one can diagonalize the matrices. In this article, we suggest an approach for diagonalizing interval matrices employing a novel methodology called the pairing technique, which will make it simpler and more eﬀective to classify and investigate interval matrices. This is extremely useful because computations involving a diagonalizable matrix can often be reduced to much simpler computations involving the corresponding diagonal matrix. We also discuss two real world applications on planar systems and linear discrete dynamical systems.

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Design and applications of interval observers for uncertain dynamical systems

Cited by 37 publications

References 110 publications

Interval observer design for nonlinear systems using simplified contraction theory

Interval observer design for nonlinear systems using simplified contraction theory

Interval observer design for nonlinear discrete‐time dynamic systems

Diagonal canonical form of interval matrices and applications on dynamical systems

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