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

Muzaffer Ates; Nezir Kadah

doi:10.11121/ijocta.01.2021.001073

Authors

Muzaffer Ates Departments of Electrical-Electronics Engineering, University of Van Yuzuncu Yil, Turkey https://orcid.org/0000-0002-4394-0815
Nezir Kadah Departments of Electrical-Electronics Engineering, Adana Alparslan Turkes Science and Technology University, Turkey https://orcid.org/0000-0001-9320-1140

DOI:

https://doi.org/10.11121/ijocta.01.2021.001073

Keywords:

Lyapunov stability, nonlinear systems, passivity, Gronwall’s inequality

Abstract

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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Author Biographies

Muzaffer Ates, Departments of Electrical-Electronics Engineering, University of Van Yuzuncu Yil, Turkey

received his B.Sc. degree in Electrical and Electronics Engineering from METU, Turkey. Then he received his M.Sc. and PhD degrees in applied mathematics from Van Yuzuncu Yil University, Van, Turkey. Now, he is working at Electrical and Electronics Engineering Department in Van Yuzuncu Yil University. His research areas are nonlinear systems, mathematical control theory, circuit theory and Lyapunov stability theory.

Nezir Kadah, Departments of Electrical-Electronics Engineering, Adana Alparslan Turkes Science and Technology University, Turkey

received his B.Sc. degree from Mersin University, Mersin, Turkey, in 2012 and his M.Sc. degree from Van Yuzuncu Yil University, Van, Turkey, in 2019. He is currently a PhD student of Electrical and Electronics Engineering at Adana Alparslan Turkes Science and Technology University (ATU), since 2019. He is also working at the department of Information Technology of ATU as the system and network administrator. His research areas are nonlinear systems, system identification, and control theory.

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