一类网络控制系统的稳定性设计

Stability design for a class of networked control systems

针对一类具有等式约束的网络控制系统控制器、采样周期以及最大允许延迟时间的设计问题,采用李亚普诺夫函数、线性矩阵不等式的方法,推导出了该网络控制系统渐近稳定的充分条件。根据此充分条件,通过建立并求解一个凸优化问题,得到网络控制系统的最大允许传输间隔以及此时的控制器,进而利用最大允许传输间隔,对采样周期进行设计并获得系统的最大允许延迟时间。通过给出一个具体的数值和仿真实例说明了此设计方法是有效的。

For a class of networked control systems （NCS） with equality constraint, this paper addresses the problem of designing controller, sampling period and the maximum allowable delay bound （MADB）. The Lyapunov function, linear matrix inequality （LMI） methods are used to derive a sufficient condition, which can guarantee that the NCS is asymptotically stable. Based on that fact, in terms of convex optimization techniques, the maximum allowable transfer interval （MATI） and controller are obtained. The MATI can be used as the rule to determine data sampling period and the MADB. Finally, the numerical and simulation example illustrate the validity of the proposed method.