New results on the global asymptotic stability of certain nonlinear RLC circuits

Ateş, Muzaffer; Laribi, Samira

doi:10.3906/elk-1612-100

Cited by 5 publications

(7 citation statements)

References 16 publications

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“…Thus, the energy functions E 1 , E 2 , and E 3 are bounded. This also implies that all the motions of ( 4), (6), and ( 8) are bounded in magnitude. Hence, the related systems (or circuits) are strongly passive.…”

Section: Nonlinear Capacitormentioning

confidence: 83%

“…Thus, system (6) with its Lyapunov function satisfies all the assumptions of Theorem 2. Therefore, (6) or the related circuit is lossless due to the trivial solution which occurs at infinity.…”

Section: Nonlinear Inductormentioning

confidence: 99%

“…Hamiltonian and Lagrangian systems comply with conservative systems (exact differential equations), but Lyapunov stability theory can be applicable to arbitrary differential equations. Thus, the Lyapunov direct method is *Corresponding Author the most common and efficient tool for stability analysis [4][5][6][7]. In this context, many elegant studies on the qualitative behavior of systems can be recorded in the literature.…”

Section: Introductionmentioning

confidence: 99%

“…These improvements will take place in section 4. In addition, [6] does not involve the passivity analysis, the notion of power -energy relationship constructing Lyapunov functions, and equation ( 1) and its implications. The present work includes these and some improvements.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Novel stability and passivity analysis for three types of nonlinear LRC circuits

Ateş¹,

Kadah²

2021

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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In this paper, the global asymptotic stability and strict passivity of three types of nonlinear RLC circuits are investigated by utilizing the Lyapunov direct method. The stability conditions are obtained by constructing appropriate Lyapunov function, which demonstrates the practical application of the Lyapunov theory with a clear perspective. The meaning of Lyapunov functions is not clear by many specialists whose studies based on Lyapunov theory. They construct Lyapunov functions by using some properties of Lyapunov functions with much trial and errors or for a system choose candidate Lyapunov functions. So, for a given system Lyapunov function is not unique. But we insist that Lyapunov (energy) function is unique for a given physical system. In this study we highly simplified Lyapunov’s direct method with suitable tools. Our approach constructing energy function based on power-energy relationship that also enable us to take the derivative of integration of energy function. These aspects have not been addressed in the literature. This paper is an attempt towards filling this gap. The results are provided within and are of central importance for the analysis of nonlinear electrical, mechanical, and neural systems which based on the system energy perspective. The simulation results given from Matlab successfully verifies the theoretical predictions.

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Section: Nonlinear Capacitormentioning

confidence: 83%

Section: Nonlinear Inductormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Novel stability and passivity analysis for three types of nonlinear LRC circuits

Ateş¹,

Kadah²

2021

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…The Lyapunov method is used to determine the stability of an equilibrium point or motion of a system using an energy function, typically a quadratic function. In the current case, this method is applied to a nonlinear system that switches between two states [14][15][16][17].…”

Section: Control and Stabilitymentioning

confidence: 99%

Photovoltaic Microinverter Based on Buck-Boost Converter and Discharge Circuit

Ghribi,

Ternifi,

Bachir

et al. 2024

Period. Polytech. Elec. Eng. Comp. Sci.

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This paper presents a novel topology for photovoltaic microinverters that uses a buck-boost converter coupled with a discharge circuit. The system enables efficient conversion of electrical energy from the solar panel without requiring voltage filters or step-up transformers. For its control, an exponential action control strategy is used, as it allows effective tracking of the reference voltage. The stability of the overall control and inverter system is demonstrated and detailed using the Lyapunov method. The sizing of the components used is also detailed. The performance of this topology is evaluated under various load conditions, revealing low harmonic distortion (THD) in both current and voltage, with the best THD of 1% being obtained at a power factor of 0.8. This makes it a promising solution for photovoltaic energy conversion.

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Controller design scheme for stabilization and synchronization of a class of chaotic and hyperchaotic systems in uncertain environment using SMC approach

Handa

Sharma

2018

Int. J. Dynam. Control

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New results on the global asymptotic stability of certain nonlinear RLC circuits

Cited by 5 publications

References 16 publications

Novel stability and passivity analysis for three types of nonlinear LRC circuits

Novel stability and passivity analysis for three types of nonlinear LRC circuits

Photovoltaic Microinverter Based on Buck-Boost Converter and Discharge Circuit

Controller design scheme for stabilization and synchronization of a class of chaotic and hyperchaotic systems in uncertain environment using SMC approach

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