Exponential stability of integral delay systems and its application to memory‐based controller design

Abstract In this paper, the problem of exponential stability is studied for a class of integral systems with multiple delays. A novel integral inequality with multiple weighting matrices is first proposed. It is theoretically shown that the newly derived integral inequality provides a tighter lower bound than existing ones based on variants of the conventional Jensen integral inequality. By utilizing the newly derived integral inequality and by constructing an improved Lyapunov–Krasovskii functional, tractable delay‐dependent conditions are derived to ensure exponential stability of the system with a prescribed decay rate. An application to the design problem of a predictor‐based controller for input delayed systems is also presented. Numerical examples are given to illustrate the effectiveness and significant improvement of the obtained results.