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In control systems, the Laplace transform is often used to analyze the stability and the performance of LTI system. For instance, the LTI system is stable if and only if the transfer function, which is the quotient between the Laplace transform of the output of the system and the Laplace transform of the input, has all of its poles in the left half complex plane.

Does wavelet transforms also found applications in analysis or design of control systems?

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In the paper Haar-Based Stability Analysis of LPV Systems, the Haar wavelet transform theory have been used to design linear matrix inequalities (LMIs) to analyze the stability of LPV systems.

As the resolution level of the Haar wavelet increases, the number of variables and rows of the designed LMI increases and the feasibility of this LMI becomes a less conservative condition for the stability of the LPV system. Although the stability of LPV systems using LMIs that become less conservatives with the increase of variables and/or rows have already been proposed in the literature, the Haar-based approach can handle a larger class of parametric dependencies as well as non-convex parametric domains.

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