# Effect of switching uncertainty on a boost converter under a coloured noise influence

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## Abstract

The noise processes associated with dynamical systems have limited bandwidth having finite, non-zero correlation time enabling us to model them as the Ornstein–Uhlenbeck process. The confluence of the deterministic system dynamics with these noisy forcing functions may trigger a series of unwarranted complex, peculiar phenomenon or stability issues in the system under different initial conditions and noise intensities. Thus, revisiting the system dynamics in the Ornstein–Uhlenbeck setting using the estimation and filtration algorithms seems an accurate and imperative choice. The Itô calculus, a very powerful classical tool, is used to evaluate the performance of stochastic differential equations. However, the Itô calculus cannot be directly applied to the systems under the influence of the Ornstein–Uhlenbeck process and we come across what is more fondly called as the curse of dimensionality, the augmented state vector approach. This paper develops a system theoretic-estimation algorithm for a switched-mode DC–DC power converter driven by the Ornstein–Uhlenbeck process. This is a novel attempt in this research direction. The algorithm is tested under a various data set and initial conditions to validate the findings.

### Keywords

Switched-mode DC–DC power converters Ornstein–Uhlenbeck process Itô theory State estimations## Notes

### Acknowledgments

The authors are grateful to finer and in-depth comments of anonymous qualified *Reviewers*. Corrections on the lines of the suggestions of the Reviewers and the Editor led to the error-less content of the ‘revised paper’.

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