State Estimation for a Class of Singular Systems Using Shifted Legendre Polynomials

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. These two methods make easy the system of state equations by turning it into the solution of a set of linear algebraic equations. The advantage of these algorithms is their easy implementation in a digital computer, and also 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.