Application of free matrix based integral inequality: sampled-data multi-agent system

Abstract

This paper analyzes the stability of sampled-data multi-agent systems with a weighted consensus protocol by the use of looped-functional and free matrix based integral inequality. In the existing stability analysis of the multi-agent system, the typical Lyapunov-functional was used, but a less conservative solution can be obtained by using the looped-functional which is developed for the single-agent system. In addition, when analyzing the stability using Lyapunov-functional, integral inequality is used to obtain the upper bound of the integral term. A larger maximum sampling interval can be obtained by using the free matrix based integral inequality which is developed in time-delay system recently. Therefore, in this paper, the Lyapunov-functional including the looped-functional was constructed, the stability condition was relaxed using the free matrix based integral inequality, and the system was confirmed to be stable at the larger sampling interval compared to the existing literature through experimental examples.