Abstract: A series of piecewise multiple general orthogonal polynomials (PMGOP) is introduced. Main properties of PMGOP are given And the series of PMGOP is applied to state analysis for linear time-invariant and time-varying systems. Relevant recursive algorithms are presented. By using the approximative technique via piecewise multiple orthogonal polynomials with low order, the method gsven in the paper has the following advantages: the amount of computation is less, computing time is less, the accuracy is higher and the algorithms are recursive.