基于采样数据的Lurie系统状态反馈控制器设计

Sampled-data-based design of state feedback controllers for Lurie systems

  • 摘要: 针对具有网络诱导时延(NID)的 Lurie 网络控制系统稳定性问题,为降低稳定性条件的保守性、提升控制器求解效率并最大化系统最大允许采样间隔,本文提出了一种低保守性设计方案。首先,考虑 NID 的时变特性,构建双边闭环Lyapunov 泛函,充分利用泛函中的不同状态之间的关系,推导出确保闭环系统绝对稳定的充分条件。为更进一步降低结果的保守性,本文在引入零等式时提出了一种新的参数化构造方式;其次,针对稳定性条件中存在的非线性耦合项,应用改进的锥互补线性化(CCL)迭代算法,通过引入新变量将非凸问题转化为线性矩阵不等式(LMI)可解问题,并通过改进迭代条件来确定控制器增益。最后,通过两个数值算例开展对比仿真验证。结果表明,与现有同类方法相比,本文所提方案能够得到保守性更低的稳定判据,同时大幅减少算法迭代次数。有效兼顾了系统稳定性分析精度与控制器求解效率。

     

    Abstract: Aiming at the stability problem of Lurie networked control systems with network-induced delay (NID), we proposes a low-conservatism design scheme to reduce the conservatism of stability conditions, improve the solution efficiency of the controller, and maximize the maximum allowable sampling interval of the system. Firstly, considering the time-varying characteristics of NID, a two-sided looped Lyapunov functional is constructed, which fully utilizes the relationships between different states in the functional to derive sufficient conditions for ensuring the absolute stability of the closed-loop system. To further reduce the conservatism of the results, a new parameterized construction method is proposed when introducing zero equalities. Secondly, targeting the nonlinear coupling terms existing in the stability conditions, an improved cone complementarity linearization (CCL) iterative algorithm is applied. By introducing new variables, the non-convex problem is converted into a problem solvable via linear matrix inequalities (LMIs), and the controller gain is determined by improving the iterative conditions. Finally, two classical numerical examples are carried out for comparative simulation verification. The results demonstrate that, compared with existing similar methods, the proposed scheme can obtain stability criteria with lower conservatism, significantly reduce the number of algorithm iterations, and effectively balance the accuracy of system stability analysis and the efficiency of controller solution.

     

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