This paper investigates the exponential stability of uncertain time delay systems using a novel descriptor redundancy approach based on delay partitioning. First, the original system is casted into an equivalent descriptor singular state–space representation by introducing redundant state variables so that the resulting delay is progressively reduced. From the equivalent model and applying Lyapunov Functional method, a sufficient condition based on Linear Matrix Inequalities (LMIs) for exponential stability with guaranteed decay rate performance is obtained. As a result, the inherent conservatism of Lyapunov–Krasovskii functional techniques can arbitrarily be reduced by increasing the number of delay partition intervals including decay rate performance and model uncertainties in polytopic form. Various benchmark examples are provided to validate the effectiveness of the proposed method, showing better trade-off between conservatism and performance in comparison to previous approaches.

本文采用基于延迟划分的新型描述符冗余方法研究了不确定时滞系统的指数稳定性。首先，通过引入冗余状态变量，将原始系统转换为等效的描述符奇异状态空间表示，以便逐渐减少最终的延迟。通过等效模型并应用Lyapunov泛函方法，获得了基于线性矩阵不等式（LMI）的足够的条件，以确保指数稳定性和衰减率性能。结果，可以通过增加延迟分配间隔的数量来任意减少Lyapunov–Krasovskii功能技术的固有保守性，包括衰减率性能和多位形式的模型不确定性。