二阶凸优化不等式及加性时变时滞系统的稳定性研究

Study on second order convex optimization inequality and stability for delay systems with two additive time-varying delays

主要研究加性时变时滞系统的时滞依赖稳定性问题.首先针对二次型凸优化函数不等式,提出新的等价不等式条件.然后,通过构造适合系统的李雅普诺夫泛函,并在其沿系统状态求导的过程中,利用改进的Jensen不等式以及本文提出的二次型凸优化函数不等式进行放缩,分析得到稳定性的线性矩阵不等式条件.最后,通过数值仿真实例,证明本文所得方法的有效性和优越性.

We studies the delay dependent stability problem of the system with two additive time-varying dela. It firstly establishes a second order convex optimization inequality, which is equivalent to the second order covex function. Secondly, a new constructed Lvapunov functional is constructed based on the additive time-varying delays property. Using the integral inequality and some other inequality technique to the derivative of the Lyapunov functionals, the delay-dependent stability condition is obtained which in terms of linear matrix inequalities. Finally, one numerical example is given to verify the effectiveness of the proposed method and the superiority of the results.