Stability Analysis of DC-DC Converters Applying Lie Algebra

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.