Stability and Stabilization of Fractional-Order Linear Systems Subject to Input Saturation

Lim, Young‐Hun; Oh, Kwang‐Kyo; Ahn, Hyo‐Sung

doi:10.1109/tac.2012.2218064

Cited by 113 publications

(57 citation statements)

References 12 publications

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“…The most frequently used definitions for noninteger derivatives are Riemann-Liouville, Grünwald-Letnikov, and Caputo definitions [6,9,[23][24][25][26][27][28][29][30][31][33][34][35][36][37][38]. As the Caputo fractional operator is more consistent than another ones, then this operator will be employed in the rest of this paper.…”

Section: Remarkmentioning

confidence: 99%

“…The output of the physical actuator has maximum and minimum amplitude limits [1,15]. Moreover, in the control literature, few results are available for systems with saturation nonlinearities [1,15,22,36]. In [1], the problem of adaptive tracking control has been investigated for a class of uncertain pure-feedback nonlinear time-delay systems in the presence of unknown asymmetric saturation actuators by means of a Gaussian error function-based continuous differentiable model.…”

Section: Introductionmentioning

confidence: 99%

“…In [1], the problem of adaptive tracking control has been investigated for a class of uncertain pure-feedback nonlinear time-delay systems in the presence of unknown asymmetric saturation actuators by means of a Gaussian error function-based continuous differentiable model. In [36], a method has been provided for the asymptotic stabilization of fractionalorder systems with input saturation. The major limitation of the adaptive controllers introduced in [1,18,36] is that all of the state variables of the systems must be measurable.…”

Section: Introductionmentioning

confidence: 99%

“…In [36], a method has been provided for the asymptotic stabilization of fractionalorder systems with input saturation. The major limitation of the adaptive controllers introduced in [1,18,36] is that all of the state variables of the systems must be measurable. • Unavailability of state measurements: In most practical situations, the state variables of the system may be unavailable for measurement [2,8,20,21].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation

Zouari

Boulkroune

Ibeas

et al. 2016

Neural Comput & Applic

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This paper focuses on the adaptive neural output feedback control of a class of uncertain multi-input-multioutput nonlinear time-delay non-integer-order systems with unmeasured states, unknown control direction, and unknown asymmetric saturation actuator. Thus, the mean value theorem and a Gaussian error function-based continuous differentiable model are used in the paper to describe the unknown asymmetric saturation actuator and to get an affine model in which the control input appears in a linear fashion, respectively. The design of the controller follows a number of steps. Firstly, based on the semigroup property of fractional-order derivative, the system is transformed into a normalized fractional-order system by means of a state transformation in order to facilitate the control design. Then, a simple linear state observer is constructed to estimate the unmeasured states of the transformed system. A neural network is incorporated to approximate the unknown nonlinear functions while a Nussbaum function is used to deal with the unknown control direction. In addition, the strictly positive real condition, the Razumikhin Lemma, the frequency-distributed model, and the Lyapunov method are utilized to derive the parameter adaptive laws and to perform the stability proof. The main advantages of this work are that:(1) it can handle systems with constant, time-varying, and distributed time-varying delays, (2) the considered class of systems is relatively large, (3) the number of adjustable parameters is reduced, (4) the tracking errors converge asymptotically to zero and all signals of the closed-loop system are bounded. Finally, some simulation examples are provided to demonstrate the validity and effectiveness of the proposed scheme.

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Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation

Zouari

Boulkroune

Ibeas

et al. 2016

Neural Comput & Applic

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“…In spite of the interest in FO dynamical system in modeling and control [3][4][5][6], only a few papers were devoted to saturation nonlinearity [7,8]. Lim et al [7] obtained the sufficient stability based on the solution of the fractional linear equation. They adopted the Gronwall-Bellman lemma and the property of sector bounded saturation in the general case with 0 < α < 2, where α represents the fractional order.…”

Section: Introductionmentioning

confidence: 99%

An extension of estimation of domain of attraction for fractional order linear system subject to saturation control

Shahri

Alfi

Machado

2015

Applied Mathematics Letters

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a b s t r a c tThis paper employs the Lyapunov direct method for the stability analysis of fractional order linear systems subject to input saturation. A new stability condition based on saturation function is adopted for estimating the domain of attraction via ellipsoid approach. To further improve this estimation, the auxiliary feedback is also supported by the concept of stability region. The advantages of the proposed method are twofold: (1) it is straightforward to handle the problem both in analysis and design because of using Lyapunov method, (2) the estimation leads to less conservative results. A numerical example illustrates the feasibility of the proposed method.

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Introduction

2017

Robust Adaptive Control for Fractional‐Order Systems With Disturbance and Saturation

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Stability and Stabilization of Fractional-Order Linear Systems Subject to Input Saturation

Cited by 113 publications

References 12 publications

Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation

Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation

An extension of estimation of domain of attraction for fractional order linear system subject to saturation control

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