@article{Razavinasab_Vali_Samavat_2024, title={State Estimation for a Class of Singular Systems Using Shifted Legendre Polynomials}, volume={10}, url={https://oiccpress.com/Majlesi-Journal-of-Electrical-Engineering/article/state-estimation-for-a-class-of-singular-systems-using-shifted-legendre-polynomials/}, abstractNote={For linear time-invariant continuous-time singular systems, two new simple approaches, the Kronecker method and the recursive method, are developed in order to estimate the states from the system input-output information via shifted Legendre polynomials (SLP) and a simple observer in the descriptor form. Sufficient conditions for the existence of the present observer are given. The two methods simplify the system of state equations into the solution of a set of linear algebraic equations. Furthermore, the proposed algorithms can be easily implemented in a digital computer and the solutions can be obtained for any length of time. Further, these approaches include the filtering and the smoothing effect which can reduce the influence of zero-mean measurement noise on estimation. Simulation results of a given numerical example demonstrate the effect of the proposed approaches.}, number={3}, journal={Majlesi Journal of Electrical Engineering}, publisher={OICC Press}, author={Razavinasab, Zahra and Vali, Mohammad Ali and Samavat, Mahmoud}, year={2024}, month={Feb.}, keywords={Descriptor observer, Shifted Legendre polynomials, Singular systems, State estimation.} }