Li Yang, Zhang Hongbin
School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, PR China.
ISA Trans. 2020 Jan;96:37-50. doi: 10.1016/j.isatra.2019.06.006. Epub 2019 Jun 12.
In this paper, the positive observer design problem is investigated for switched positive Takagi-Sugeno (T-S) fuzzy delayed systems (SPFDSs) with dwell time constraints. First, by using a clock-dependent co-positive Lyapunov-Krasovskii function (CDCLKF), sufficient conditions are derived for stability of SPFDSs with dwell time. Then, the observer design problem of SPFDSs is separately considered for the measurable and unmeasurable premise variable cases. On the basis of the obtained stability results, sufficient conditions are presented to check the existence of observers for SPFDSs with measurable and unmeasurable premise variables. Through minimizing the system matrix norm of the error dynamics, the optimized observer gains for SPFDSs with unmeasurable premise variables are achieved, and the errors between the system states and their estimations are reduced. All the clock-dependent conditions are relaxed into sum of squares (SOS) program via the SOS approximation approach. At last, two examples are given to show the validity of our results.
本文研究了具有驻留时间约束的切换正Takagi-Sugeno（T-S）模糊时滞系统（SPFDSs）的正观测器设计问题。首先，通过使用与时钟相关的共正Lyapunov-Krasovskii函数（CDCLKF），推导了具有驻留时间的SPFDSs稳定性的充分条件。然后，分别针对可测和不可测前提变量情况考虑了SPFDSs的观测器设计问题。基于所获得的稳定性结果，给出了检查具有可测和不可测前提变量的SPFDSs观测器存在性的充分条件。通过最小化误差动态的系统矩阵范数，获得了具有不可测前提变量的SPFDSs的优化观测器增益，并减少了系统状态与其估计值之间的误差。通过平方和（SOS）逼近方法，所有与时钟相关的条件都被松弛为SOS程序。最后，给出两个例子以说明我们结果的有效性。
