区间时变时滞离散系统的稳定性分析及控制器设计

发布时间：2018-07-31 19:06

【摘要】：含有区间状态时滞的系统在实际中有重要的应用,如它可以方便地描述一类网络控制系统.本文对含有区间状态时滞的线性离散系统考虑了稳定性分析与状态反馈控制器设计问题.为研究该类系统的稳定性,通过引入二重求和和三重求和构造了新型的Lyapunov-Krasovskii泛函.在对所构造的泛函处理其差分的过程中,利用了基于Abel引理的有限和不等式技术以及时滞分割方法,进而提出了该类系统稳定的线性矩阵不等式充分性条件.相对于以往的Lyapunov泛函,本文所提出的Lyapunov-Krasovskii泛函包含更多的时滞信息,而且所采用的差分处理方法不涉及原系统的模型变化,因而所提出的渐近稳定充分条件具有较低保守性.另外,相对于以前存在的自由权矩阵方法,本文所提出的方法具有较少的可行性变量矩阵,因而能有效地降低计算量.基于所提出的稳定性条件,本文进一步提出了无记忆状态反馈镇定控制器的设计方法.所提出镇定控制器设计方法也通过线性矩阵不等式给出,具有很好的数值稳定性.最后,通过数值算例验证了所提方法的正确性和有效性.
[Abstract]:Systems with interval state delays have important applications in practice, for example, they can describe a class of networked control systems conveniently. In this paper, stability analysis and state feedback controller design are considered for linear discrete systems with interval state delays. In order to study the stability of this class of systems, a new Lyapunov-Krasovskii functional is constructed by introducing double summation and triple summation. In the process of dealing with the difference of the constructed functional, the finite sum inequality technique based on Abel Lemma and the time-delay partition method are used, and then the sufficient conditions for the stability of this class of systems are proposed. Compared with the previous Lyapunov Functionals, the Lyapunov-Krasovskii Functionals presented in this paper contain more delay information, and the difference processing method does not involve the model changes of the original system, so the asymptotic stability sufficient conditions proposed in this paper are of low conservatism. In addition, compared with the previous free matrix method, the method presented in this paper has less feasible variable matrix, so it can effectively reduce the computational complexity. Based on the stability conditions proposed in this paper, a design method of memoryless state feedback stabilization controller is proposed. The proposed stabilization controller design method is also given by linear matrix inequality (LMI), which has good numerical stability. Finally, the validity and validity of the proposed method are verified by numerical examples.
【作者单位】：哈尔滨工业大学深圳研究生院;深圳职业技术学院;
【基金】：国家自然科学基金重大项目(61690210,61690212);国家自然科学基金(61603111)
【分类号】：TP13

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