Direct methods are applied to solve linear time-varying delay systems based on vector forms of block-pulse functions (BPFs) and triangular functions (TFs). Operational matrices of integration of BPFs and TFs are applied to transform linear time-varying delay systems to a linear set of algebraic equations. Further, some numerical examples are provided to indicate reliability and the accuracy of these methods. Convergence analysis of the proposed method has been discussed.

中文翻译：

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解决时变时滞系统的直接方法

基于块脉冲函数（BPF）和三角函数（TF）的矢量形式，直接方法被用于求解线性时变延迟系统。BPF和TF积分的运算矩阵可用于将线性时变时滞系统转换为线性代数方程组。此外，提供了一些数值示例来指示这些方法的可靠性和准确性。已经讨论了所提出方法的收敛性分析。