New Weighted Integral Inequalities and Its Application to Exponential Stability Analysis of Time-Delay Systems

Abstract

This paper is concerned with the exponential stability analysis for time-delay systems. First, two new weighted integral inequalities are presented based on the auxiliary function-based integral inequalities. In the new weighted integral inequalities, unlike previous studies, exponentially weighted integral vectors are used to find the lower bounds of the weighted integral quadratic terms. Then, by utilizing the new weighted integral inequalities, a new linear matrix inequality (LMI) condition is derived for the exponential stability of the considered time-delay systems. Finally, the numerical examples are conducted to validate the effectiveness of the new LMI condition. The example results show that the LMI condition derived in this paper is less conservative than existing ones in analyzing exponential stability of the considered systems.

Keywords

• Time-delay systems
• exponential stability analysis
• Lyapunov–Krasovskii functional
• linear matrix inequalities