Modelling and simulation of nabla fractional dynamic systems with nonzero initial conditions

Wei, Yiheng; Wang, Jiachang; Tse, Peter W.; Wang, Yong

doi:10.1002/asjc.2232

Cited by 20 publications

(19 citation statements)

References 37 publications

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“…The adopted numerical calculation algorithm is modified from the approximation method in [52]. Firstly, setting the input Secondly, setting the input v(k) = (1 + ω l ) a−k , the output satisfies x(k) =…”

Section: Simulation Studymentioning

confidence: 99%

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Limited frequency band diffusive representation for nabla fractional order transfer functions

2021

Turk J Math

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Though infinite-dimensional characteristic is the natural property of nabla fractional order systems and it is the foundation of stability analysis, controller synthesis and numerical realization, there are few research focusing on this topic. Under this background, this paper concerns the diffusive representation of nabla fractional order systems. Firstly, several variants are developed for the elementary equality in frequency domain, i.e., 1 s α = +∞ 0 µα(ω) s+ω dω . Afterwards, the limited frequency band diffusive representation and the unit impulse response are derived for a series of nabla fractional order transfer functions. Finally, an attempt to find the diffusive representation for general nabla fractional order transfer functions is made. Some conclusions are presented.

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Section: Simulation Studymentioning

confidence: 99%

“…Afterwards, the converse theorem for indirected Lyapunov method was established in [45]. By using the discretization approach, the numerical approximation method was proposed in [52]. However, this method in nabla discrete time case does not draw enough attention.…”

Section: Introductionmentioning

confidence: 99%

Limited frequency band diffusive representation for nabla fractional order transfer functions

2021

Turk J Math

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“…The inverse nabla Laplace transform can be obtained as [35]

𝒩_{a}^{- 1} ({}, F false(s false)) ≜ \frac{1}{2 π i} \oint_{c} F false(s false) {false(1 - s false)}^{- k + a} d s,

where

k \in ℕ_{a + 1}

, c is a closed curve rotating around the point (1,i0) clockwise and it also locates in the convergent region of F ( s ) (defined as ()).…”

Section: Preliminariesmentioning

confidence: 99%

“…By introducing the sampling interval

h \in ℝ_{+}

, a comprehensive and groundbreaking work was done on the general derivatives, exponentials and transforms [21,22]. The numerical approximation was investigated for nabla fractional dynamic systems with nonzero initial instant and nonzero initial state [35]. To analyze the stability of discrete fractional order systems, the direct Lyapunov method was developed while the results were conservative [6,30,36].…”

Section: Introductionmentioning

confidence: 99%

Description and analysis of the time–domain response of nabla discrete fractional order systems

Wei

Gao

Cheng

et al. 2020

Asian Journal of Control

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This paper investigates the time-domain response of nabla discrete fractional order systems by exploring several useful properties of the nabla discrete Laplace transform and the discrete Mittag-Leffler function. In particular, we find the limitation of discrete Mittag-Leffler when adopted in describing the response.Then we establish two fundamental properties of a nabla discrete fractional order system with nonzero initial instant: i) the existence and uniqueness of the system time-domain response; and ii) the dynamic behavior of the zero input response. Finally, a simulation study is provided to show the validity of the theoretical results.

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“…Modeling problems are important issues in many applications, especially in control systems design [13–16]. Furthermore, probability models are efficient for modeling a dynamic system [17].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy‐HMM modeling for emotion detection using electrocardiogram signals

Pan

2020

Asian Journal of Control

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In this paper, a Fuzzy Hidden Markov Model (FHMM) for electrocardiogram (ECG)-based emotion recognition is proposed. The FHMM model is modeled using the fuzzy membership of each class of feature vectors to compute the elements of the matric in the model. Each element in the matric is determined by the two nearest classes of feature vectors with fuzzy classification to avoid the winner-takes-all situation that usually happens in tradition discrete Hidden Markov Models (HMM) and that reduces the accuracy of the modeling results. The FHMM modeling proposed in this paper can improve the precision of traditional discrete HMM modeling. Also, the features for emotion recognition, which are selected according to those used in prior research, are calculated from ECG signals. The selected features form a feature vector and these are calculated for all ECG signals. Some feature vectors are used to train the FHMM model and the remaining are used for testing. Experimental results show that the proposed FHMM model can achieve impressive improvements on the three indices, sensitivities (Se%), positive predictive value (PPV%), and total classification accuracy (TCA%), compared to traditional HMM. Moreover, compared to some existing studies, the recognition rates of the proposed method are higher. These results verify the efficiency of the proposed method for emotion recognition from ECG signals.

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Modelling and simulation of nabla fractional dynamic systems with nonzero initial conditions

Cited by 20 publications

References 37 publications

Limited frequency band diffusive representation for nabla fractional order transfer functions

Limited frequency band diffusive representation for nabla fractional order transfer functions

Description and analysis of the time–domain response of nabla discrete fractional order systems

Fuzzy‐HMM modeling for emotion detection using electrocardiogram signals

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