带输入饱和的奇异摄动双线性系统的无源控制

针对具有输入约束和变时滞的奇异摄动双线性系统，提出一种状态反馈无源控制器的设计方法，以消除时滞因素和输入饱和对闭环系统的影响.首先，在Lyapunov稳定性理论和无源性理论的框架下，应用线性矩阵不等式技术和凸组合技术，将系统状态反馈控制器的设计归结为求解一组与时滞上界无关的线性矩阵不等式问题.所得控制器使闭环系统渐近稳定且无源，同时构造了与奇异摄动参数相关的椭圆吸引域估计，并将上述方法推广到不含时滞和外部输入的系统.然后，提出凸优化问题，得到闭环系统吸引域的极大估计，其中奇异摄动参数稳定界也是设计的目标之一.最后，通过数值仿真算例说明了所提理论方法的有效性.

Passive Control of Singularly Perturbed Bilinear Systems with Input Saturation

For singularly perturbed bilinear systems with input constraints and time-varying delays， a design method of state feedback passive controller is proposed to eliminate the effects of delay factors and input saturation on the closed-loop system. Firstly， in the framework of Lyapunov stability theory and passivity theory， using linear matrix inequality technology and convex combination technology， the design of the system state feedback controller is reduced to solve a set of linear matrix inequalities independent of the upper bound of time delay. The obtained controller makes the closed-loop system asymptotically stable and passive， and constructs the estimation of the elliptic domain of attraction related to singular perturbation parameters. The above method is extended to the system without time delay and external input. Then， a convex optimization problem is proposed to obtain the maximum estimation of the domain of attraction of the closed-loop system， and the stability bound of singular perturbation parameter is also one of the design objectives. Finally， numerical simulation examples illustrate the effectiveness of the proposed theoretical method.