A wavelet-based approach for stability analysis of periodic delay-differential systems with discrete delay

This paper presents a semi-analytical wavelet-based approach for stability analysis of time-periodic delay-differential equations (DDEs) with a single discrete time delay. By using the autocorrelation functions of compactly supported Daubechies scaling functions, the DDE is discretized to a set of algebraic equations, employing the wavelet collocation method. The state transition matrix over a single period is constructed to determine the stability based on Floquet theory. Stability charts for the one-degree-of-freedom milling model and time-delayed Mathieu equation are obtained, illustrating both the efficiency and accuracy of the proposed approach.

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