This paper deals with the parameter estimation of an important class of nonlinear time-delay systems with a piecewise constant delay function. The developed procedure is based on a generalization of the hybrid of block-pulse functions and Taylor polynomials. The operational matrix of integration related to the generalized hybrid functions is constructed. Furthermore, an upper bound with respect to the L²-norm for the generalized hybrid functions is acquired, and convergence of the generalized hybrid functions is demonstrated. The merits of the hybrid basis are implemented to convert the problem under examination into an algebraic system. The methodology of least squares is adopted for solving the acquired algebraic system. An illustrative example is included in order to validate the efficiency and accuracy of the designed method. It is shown that the proposed approach provides accurate estimates for the desired parameters. The current approach reduces the computation complexity of the identification process.

中文翻译：

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一类具有分段常时滞的非线性多时滞系统的参数辨识

本文处理一类重要的具有分段常数延迟函数的非线性时滞系统的参数估计。开发的程序基于块脉冲函数和泰勒多项式的混合的推广。构造了与广义混合函数相关的积分运算矩阵。此外，关于L ^2的上界获得了广义混合函数的-范数，证明了广义混合函数的收敛性。实现了混合基的优点，以将所检查的问题转换为代数系统。得到的代数系统采用最小二乘法求解。包括一个说明性示例，以验证所设计方法的效率和准确性。结果表明，所提出的方法为所需参数提供了准确的估计。当前的方法降低了识别过程的计算复杂度。