An Improved Stability Theorem for Nonlinear Systems on Time Scales With Application to Multi-Agent Systems
Xiaodong Lü, Haitao Li
Abstract
In this brief, stability analysis of nonlinear systems on time scales is further investigated. The traditional stability theorems require the time-scale derivative of related Lyapunov function to be negative, which are conservative. Based on the induction principle on time scales, an improved stability theorem is proposed in this brief by introducing the time-scale type uniformly asymptotically stable function. It is shown that this improved stability theorem weakens the negativity restriction on the time-scale derivative of related Lyapunov function. Then, this improved stability theorem is applied to solve consensus problem of multi-agent systems on time scales. A numerical example is given to illustrate the effectiveness of the theoretic results.