Qian Wei, Yuan Manman, Wang Lei, Bu Xuhui, Yang Junqi
School of Electrical Engineering and Automation, Henan Polytechnic University, 454000 Henan, China.
School of Automation Science and Electrical Engineering, Beihang University, 100191 Beijing, China.
ISA Trans. 2017 Sep;70:1-6. doi: 10.1016/j.isatra.2017.05.017. Epub 2017 Jun 3.
The paper considers the stabilization for systems with interval time-varying delay. By decomposing the delay interval into multiple equidistant subintervals and considering the triple integral terms, a novel Lyapunov-krasovskii functional(LKF) is defined. Then extended integral inequality and convex combination approach are used to estimate the derivative of the constructed functional, and as a result, the new stability criterion with less conservatism and decision variables is obtained. On this basis, the state feedback controller is designed, by using linearization method, the existence condition of controller is obtained in terms of linear matrix inequalities(LMIs), and the specific form of controller is also given, moreover, by selecting the appropriate parameter value, the stabilization time of the system can be reduced. Numerical examples are given to illustrate the effectiveness of the proposed method.
本文考虑了具有区间时变延迟系统的镇定问题。通过将延迟区间分解为多个等距子区间并考虑三重积分项，定义了一种新颖的Lyapunov-Krasovskii泛函（LKF）。然后利用扩展积分不等式和凸组合方法估计所构造泛函的导数，从而得到了具有较少保守性和决策变量的新稳定性判据。在此基础上，设计了状态反馈控制器，通过线性化方法，根据线性矩阵不等式（LMI）得到了控制器的存在条件，并给出了控制器的具体形式，此外，通过选择合适的参数值，可以缩短系统的镇定时间。给出了数值算例来说明所提方法的有效性。
