基于改进的Lyapunov泛函的时变时滞系统稳定判据

On the Stability Criteria for Time-Varying Delay Systems Based on Improved Lyapunov Function

针对时变时滞系统的延迟依赖稳定性问题进行了研究。选取一个合适的Lyapunov泛函,把Lyapunov函数中某些积分项进行修改并增加一个积分项;通过将基于自由矩阵积分不等式得到的部分矩阵的松弛条件,与二阶Bessel-Legendre积分不等式相结合来得到改进的结果。数值实例验证了此方法的保守性和优越性。

An investigation has been conducted on the flaw of delay-dependent stability found in time-vary delay systems, followed by the selection of a suitable Lyapunov function, with a modification of some integral terms in Lyapunov function and the addition of an integral term. The improved results can be obtained by combining the relaxation conditions of partial matrices based on free matrix integral inequalities with the second-order Bessel- Legendre integral inequalities. The conservativeness and superiority of this proposed method can be verified by numerical examples.