Functional interval observer design for singular fractional-order systems with disturbances

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331220944897 ◽

2020 ◽

pp. 014233122094489

Author(s):

Dinh Cong Huong ◽

Dao Thi Hai Yen

Keyword(s):

Fractional Order ◽

Design Method ◽

Observer Design ◽

Effective Algorithm ◽

Fractional Order Systems ◽

Full State ◽

Simulation Results ◽

Interval Observer ◽

Interval Observers ◽

State Functions

In this study, we consider the problem of designing functional interval observers for a class of singular fractional-order systems. The goal of this work is to design not a full state interval observer for singular fractional-order systems, but to design an observer for state functions of this kind of systems. Conditions for the existence of such functional interval observers are given and an effective algorithm for computing unknown observer matrices is provided in this study. Two numerical examples and simulation results are provided to illustrate the effectiveness of the proposed design method.

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Functional interval observers for nonlinear fractional-order systems with time-varying delays and disturbances

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1177/0959651820945828 ◽

2020 ◽

pp. 095965182094582

Author(s):

Dao Thi Hai Yen ◽

Dinh Cong Huong

Keyword(s):

Time Delay ◽

Fractional Order ◽

Design Method ◽

Delay Systems ◽

Time Varying ◽

Time Delay Systems ◽

Fractional Order Systems ◽

Integer Order ◽

Interval Observer ◽

Interval Observers

This article considers the estimation problem for a class of uncertain fractional-order systems with time-varying delays and disturbances, in which the time-varying delays are present in the state, while the disturbances are present in the output. A new design method of functional interval observers is proposed. In contrast to interval observers currently available in the literature, which dealt with integer-order systems or fractional-order systems without time delays, the functional interval observers with fractional-order [Formula: see text] in this article can deal with fractional-order time-delay systems and integer-order time-delay systems (when [Formula: see text]). Existence conditions of functional interval observers for non-linear fractional-order systems with time-varying delays are established and they are formulated in terms of linear programmings. Two algorithms are provided for determining the functional interval observers. Illustrative examples of the functional interval observer application are presented.

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Design of distributed functional interval observers for large-scale networks impulsive systems

Transactions of the Institute of Measurement and Control ◽

10.1177/01423312211022604 ◽

2021 ◽

pp. 014233122110226

Author(s):

Dinh Cong Huong ◽

Dao Thi Hai Yen ◽

Mai Viet Thuan

Keyword(s):

State Vector ◽

Large Scale ◽

Design Method ◽

Linear Functions ◽

Effective Algorithm ◽

Impulsive Systems ◽

Simulation Results ◽

Large Scale Networks ◽

Interval Observers ◽

Bounded Uncertainties

In this paper, we consider the problem of designing distributed functional interval observers (IOs) for a class of large-scale networks impulsive systems with bounded uncertainties. We first design IOs for linear functions of the state vector of each system of the considered system. We then provide conditions for the existence of such IOs and an effective algorithm for computing unknown observer matrices. Finally, two examples and simulation results are given to illustrate the effectiveness of the proposed design method.

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A New Fractional Order Observer Design for Fractional Order Nonlinear Systems

Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B ◽

10.1115/detc2011-48861 ◽

2011 ◽

Cited By ~ 18

Author(s):

Sara Dadras ◽

Hamid Reza Momeni

Keyword(s):

Fractional Order ◽

Original System ◽

Observer Design ◽

Fractional Order Systems ◽

State Variables ◽

Lyapunov Approach ◽

Error System ◽

Simulation Results ◽

System States ◽

The Stability

In this paper, a class of fractional order systems is considered and simple fractional order observers have been proposed to estimate the system’s state variables. By introducing a fractional calculus into the observer design, the developed fractional order observers guarantee the estimated states reach the original system states. Using the fractional order Lyapunov approach, the stability (zero convergence) of the error system is investigated. Finally, the simulation results demonstrate validity and effectiveness of the proposed scheme.

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Realization of a fractional-order RLC circuit via constant phase element

International Journal of Dynamics and Control ◽

10.1007/s40435-021-00778-4 ◽

2021 ◽

Author(s):

Riccardo Caponetto ◽

Salvatore Graziani ◽

Emanuele Murgano

Keyword(s):

Experimental Data ◽

Carbon Black ◽

Fractional Order ◽

Constant Phase Element ◽

Polymeric Matrix ◽

Fractional Order Systems ◽

New Device ◽

Rlc Circuit ◽

Simulation Results

AbstractIn the paper, a fractional-order RLC circuit is presented. The circuit is realized by using a fractional-order capacitor. This is realized by using carbon black dispersed in a polymeric matrix. Simulation results are compared with the experimental data, confirming the suitability of applying this new device in the circuital implementation of fractional-order systems.

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