Finite energy Lyapunov function candidate for fractional order general nonlinear systems

Li, Yan; Zhao, Daduan; Chen, YangQuan; Podlubný, Igor; Zhang, Chenghui

doi:10.1016/j.cnsns.2019.104886

Cited by 31 publications

(11 citation statements)

References 36 publications

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“…However, as pointed out in Ref. [60], the pseudo and true states are equivalent on

t \geq t_{0}

, if the history of the system in different tests remains the same before

t_{0}

, i.e.,

x false(t false) = \overset{false~}{x} false(t false) = ϕ false(t false)

holds for

- L < t < t_{0}

, where L is the memory length,

x false(t false), \overset{false~}{x} false(t false)

are pseudo and true states, respectively. That can be done by stay still or non‐destructive preconditioning on

false[L, t_{0} false)

, and then to determine or to reset the initial state

x false(t_{0} false)

t_{0}

. Remark 8 Uncertainties are unavoidable and must be considered in system modelling, system (1) is very common mathematical model to describe uncertain linear system with structured uncertainties and time‐delay in the plant.…”

Section: Resultsmentioning

confidence: 99%

Non‐fragile control for a class of fractional‐order uncertain linear systems with time‐delay

Chen

et al. 2020

IET Control Theory & Applications

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“…However, as pointed out in Ref. [60], the pseudo and true states are equivalent on

t \geq t_{0}

, if the history of the system in different tests remains the same before

t_{0}

, i.e.,

x false(t false) = \overset{false~}{x} false(t false) = ϕ false(t false)

holds for

- L < t < t_{0}

, where L is the memory length,

x false(t false), \overset{false~}{x} false(t false)

are pseudo and true states, respectively. That can be done by stay still or non‐destructive preconditioning on

false[L, t_{0} false)

, and then to determine or to reset the initial state

x false(t_{0} false)

t_{0}

Section: Resultsmentioning

confidence: 99%

Non‐fragile control for a class of fractional‐order uncertain linear systems with time‐delay

Chen

et al. 2020

IET Control Theory & Applications

Self Cite

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“…Nevertheless, this task, due to innovative nature of finding suitable Lyapunov function candidates and the difficulties of working with fractional-order differential operators in the viewpoint of obtaining a closed form for the derivative of typical Lyapunov functions, may not be straightforward. Even though, in some research works, systematic approaches are proposed to construct Lyapunov function candidates for fractional-order systems (see for instance [66]). An effective trick to overcome the aforementioned difficulties is to use the inequalities on fractional-order derivatives of the Lyapunov function candidates that specify the upper bounds for these derivatives with respect to the fractional derivatives of the pseudo-state vector of the system (this idea has been originally proposed in [67], and then extended in other research works).…”

Section: Stability Analysis Based On Lyapunov Direct Methodsmentioning

confidence: 99%

Nonlinear Fractional-Order Circuits and Systems: Motivation, A Brief Overview, and Some Future Directions

Tavazoei

Tavakoli-Kakhki

Bizzarri

2020

IEEE Open J. Circuits Syst.

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In recent years, fractional-order differential operators, and the dynamic models constructed based on these generalized operators have been widely considered in design and practical implementation of electrical circuits and systems. Simultaneously, facing with fractional-order dynamics and the nonlinear ones in electrical circuits and systems enforces us to use more advanced tools (in comparison to those commonly used in design and analysis of linear fractional-order/nonlinear integer-order circuits and systems) for their analysis, design, and implementation. Discussing on such a motivation, this tutorial paper aims to provide an overview on the recent achievements in proposing effective tools for analysis and design of nonlinear fractional-order circuits and systems. Moreover, some open problems, which can specify future directions for continuing research works on the aforementioned subject, are discussed.

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“…However, the success of the controller function depends upon the stability measure. The positive terminal of Lyapunov function [23] can be elaborated in (21) also the process function of Lyapunov scheme is defined in (22) and (23).…”

Section: Stability Analysismentioning

confidence: 99%

Innovative and Efficient Electric Braking System In High-Speed Trains using Proportional Resonant Controller

Ravikumar*

2019

IJITEE

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The high-speed trains are eight times more efficient than traditional trains because it significantly operates faster than the other trains; however, the train accidents are happened as because of its poor braking system. From this reason, effective braking system control techniques are developed. In this paper, the electric brake regenerative system is introduced to control the high-speed train. Therefore the braking system of a high-speed train is modeled in Brushless Direct Current (BLDC) motor, which is controlled by the gain of Proportional Resonant (PR) controller. Subsequently, the parameters of the controller and error percentage from the controller in the braking system are optimized using Multi-Objective African Buffalo Optimization (MOABO). The developed controller in braking system stability is analyzing by the Lyapunov function. The results of the braking system are validating by the torque and speed of the high-speed train braking system. Furthermore, the proposed high-speed braking system control is compared with existing control techniques in a high-speed train.

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Finite energy Lyapunov function candidate for fractional order general nonlinear systems

Cited by 31 publications

References 36 publications

Non‐fragile control for a class of fractional‐order uncertain linear systems with time‐delay

Non‐fragile control for a class of fractional‐order uncertain linear systems with time‐delay

Nonlinear Fractional-Order Circuits and Systems: Motivation, A Brief Overview, and Some Future Directions

Innovative and Efficient Electric Braking System In High-Speed Trains using Proportional Resonant Controller

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