Absolute and Robust Stability Analysis for Time-varying Systems based on Reciprocally Convex Relaxation Method

This paper is concerned with the absolute and robust stability of some Lurie systems with time-varying delay. By construction of a piecewise analytical method with triple-integral terms and constructing a novel Lyapunov–Krasovskii functional, some less conservative stability criteria without extra free variables are obtained. Through using a tighter bounding inequality into the Reciprocally Coverx Relaxating(RCR) method, some sources of computational complexity, such as the general convex combination and free variables are not necessary to be adopted to estimation. So the developed criteria not only theoretically improve some existing results, but also have higher computational efficiency. Numerical examples demonstrate the effectiveness of the proposed approach.