改进Lyapunov泛函下变时滞系统稳定性分析

1)深圳信息职业技术学院机电工程学院,广东深圳518172; 2)哈尔滨工业大学深圳研究生院,广东深圳518055

区间变时滞; 倒数凸组合; 线性矩阵不等式; 稳定性判据; 改进Lyapunov泛函; Jensen积分

Stability analysis of time-varying delaysystem based on an improved Lyapunov function
Wang Xinwei1, Zhang Ying2, and Rong Yumi2

Wang Xinwei1, Zhang Ying2, and Rong Yumi21)Department of Mechanical and Electrical Engineering, Shenzhen Institute of Information Technology, Shenzhen 518172, Guangdong Province, P.R.China2)Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, Guangdong Province, P.R.China

interval time-varying delay; reciprocally convex combination; linear matrix inequality; stability criteria; Lyapunov improved functional; Jensen integration

DOI: 10.3724/SP.J.1249.2017.02181

备注

针对具有区间变时滞的线性系统,提出一种新的稳定性判据.基于改进Lyapunov泛函,采用Jensen积分不等式和倒数凸组合技术,对Lyapunov泛函导数中的积分项进行界定,获得更紧的时滞上界,从而得到保守性更低的稳定性判据.通过数值实例验证所提出的稳定性判据有效.

We provide a new delay-range-dependent criterion for interval time-varying delay linear systems. By using Jensen inequality method and reciprocally convex combination technique,the upper bound of the derivative of our improved Lyapunov function can be estimated more tightly. And then newless conservative stability criteria are derived. Numerical examples are given to illustrate the effectiveness and the improvementof the proposed criterion.

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