A novel descriptor redundancy method based on delay partition for exponential stability of time delay systems

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.