按段多重一般正交多项式系及其在线性系统状态分析中的应用

A Series of Piecewise General Orthogonal Polynomials and Its Application to State Analysis for Linear Systems

本文引入按段多重一般正交多项式系,提出了它的一些主要性质,並把它应用于线性时不变和时变系统的状态分析,给出了有关的递推算法。由于采用了按段多重低阶正交多項式逼近技术,该方法具有计算量少、计算时间短、结果精度高和可递推计算等优点。

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.