Numerical solutions of linear time-varying descriptor systems via hybrid functions

State analysis of linear time-varying descriptor systems via hybrid functions are proposed in this paper. Based upon some useful properties of hybrid functions, a special product matrix and a related coefficient matrix are applied to solve the descriptor systems. The unknown coefficient matrix will be in generalized Lyapunov equation form, which is solved via the Kronecker product method. The advantages of hybrid functions are not only the values of n and m are adjustable but also it can yield more accurate numerical solutions than orthogonal functions and orthogonal polynomials to the problems of solving the descriptor systems. We propose that the available optimal values of n and m can minimize the relative errors in the numerical solutions. The high accuracy and the wide applicability of hybrid function approach will be demonstrated with numerical examples.