广义正交多项式在卷积求解中的应用

The Application of Generalized Othogonal Polynomials (GOP) to the Solution of Convolution Integrals

本文定义了一类特殊矩阵——广义正交多项式(GOP)的分离矩阵。它应用分离矩阵的分割性质及其它GOP性质,得到了卷积求解的一类新方法。两个实例充分展示了此方法在自动控制领域中的实用价值。分离矩阵还可用在时滞系统的分析、参数估计及最优控制等方面。

By using the recursive formula of GOP, the separative matrices of GOP, which have a nice structure and an elegant recursive formula, are introduced at first time. Applying the property of the separative matrices, the paper presents a new approach to the solution of convolution integral. Two examples are included to demonstrate the validity and applicability of the approach. Moreover the separative matrices can be used for the identification of impulse response and the optimal design of linear servomechanisms as well as the analysis, parameter estimation and optimal control of systems with time-delay.