Wavelet transform for determination of state and trajectory sensitivity of a singular control system

In this paper wavelet transform is used to determine the state and trajectory sensitivity of homogeneous and non-homogeneous systems. The differential-algebraic equation describing a system is converted via wavelet transform to an algebraic generalized Lyapunov equation which is solved for the coefficients of the state variables in terms of Haar basis. Further, problems of trajectory sensitivity analysis for singular as well as nonsingular systems have also been explored using the same orthogonal basis. Finally, using Kronecker product method, a generalized program is developed to determine the state and sensitivity for any number of basis function in Haar domain.