Improved inequality-based functions approach for stability analysis of time delay system

This paper focuses on stability analysis for time delay system. By introducing appropriate intermediate polynomial, a new slack variable-dependent inequality involving double integrals of system state is constructed. Then, some novel delay-product types of inequality-based functions (IBFs) with respect to delay range are developed to exploit additional degrees of freedom and more system information, while avoiding superfluous matrices. By virtue of the suggested IBFs, an improved stability criterion is derived, in which the potential capacities of advanced bounding technique are adequately explored and the information on both delay and its derivative is sufficiently reflected. As a result, more desirable performance with admissible computational complexity is achieved by the proposed approach, which is demonstrated by the numerical examples.