Legendre Wavelets with Scaling in Time-delay Systems
Abstract
This research presents the integration, product, delay and inverse time operational matrices of Legendre wavelets with an arbitrary scaling parameter and illustrates how to design this parameter in order to improve their accuracy and capability in handling optimal control and analysis of time-delay systems. Using the presented Legendre wavelets, the piecewise delay operational matrix is derived to develop the applicability of Legendre wavelets in systems with piecewise constant time-delays or time-varying delays. With the aid of these matrices, the new Legendre wavelets method is applied on linear time-delay systems. The reliability and efficiency of the method are demonstrated by some numerical experiments.References
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