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ABSTRACT
Stability analysis of switched DC-DC converters is necessary because instability enhances current ripple and causes converter operation at unwanted voltage/current level. In the present study, stability analysis of switched converters using Lie Algebra has been performed considering the switched linear model of DC-DC converters. The switched linear system is asymptotically stable if the Lie bracket formed by the state matrices of the system is commutative. The Lie Algebra is generated and its derived series is also computed. The Lie Algebra is found to be solvable, consequently the switched system is exponentially stable under arbitrary switching. The effect of duty cycle variation and load resistance of DC-DC converters, working in continuous conduction mode (CCM) on the decay constant and decay coefficient, has also been studied. The decay coefficient and decay rate of this exponentially stable system are observed to increase with an increase in the duty cycle for a specific load resistance.
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.
SUPPLEMENTAL DATA
Supplemental data for this article can be accessed at https://doi.org/10.1080/03772063.2020.1754931
Additional information
Notes on contributors
Debanjana Bhattacharyya
Debanjana Bhattacharyya received her BTech degree in electrical engineering from B P Poddar Institute of Management and Technology, Kolkata, India in 2004 and MTech degree in Industrial Electrical Systems from National Institute of Technology, Durgapur, India in 2006. She is currently pursuing PhD at the Department of Mathematics, National Institute of Technology, Rourkela, India in nonlinear control systems and applications of differential geometry and lie algebra to control systems. Email: [email protected]
Kishor Chandra Pati
Kishor Chandra Pati is a professor in the Department of Mathematics of National Institute of Technology, Rourkela, Odisha, India. His broad area of research is lie algebra and control theory.