The problem of designing a stabilizing feedback controller in the presence of saturating actuators and multi-rate (asynchronous) aperiodic state measurements is studied. Specifically, we consider a scenario in which measurements of the plant states are collected at the controller end in a sporadic and asynchronous fashion. A hybrid controller is used to perform a fusion of measurements sampled at different times. In between sampling events, the controller behaves as a copy of the plant and provides a feedback control signal based on the reconstruction of the plant state. The presence of saturation at the plant input limits the value of the components of this signal to a bounded range. When a new measurement is available, the controller state undergoes an instantaneous jump. The resulting system is augmented with a set of timers triggering the arrival of new measurements and analyzed in a hybrid systems framework. Relying on Lyapunov tools for hybrid systems and techniques for control design under saturation, we propose sufficient conditions in the form of matrix inequalities to ensure regional exponential stability of a closed-set containing the origin of the plant, i.e., exponential stability with a guaranteed region of attraction. Specifically, explicit estimates of the basin of attraction are provided in the form of ellipsoidal sets. Leveraging those conditions, a design procedure based on semidefinite programming is proposed to design a stabilizing controller with maximized size of the basin attraction. The effectiveness of the proposed methodology is shown in an example.

研究了在存在饱和执行器和多速率（异步）非周期状态测量的情况下设计稳定反馈控制器的问题。具体来说，我们考虑这样一个场景，在该场景中，在控制器端以零星和异步的方式收集设备状态的测量值。混合控制器用于执行在不同时间采样的测量的融合。在采样事件之间，控制器充当工厂的副本，并根据工厂状态的重建提供反馈控制信号。工厂输入处饱和的存在将此信号分量的值限制在一个有界范围内。当有新的测量可用时，控制器状态会发生瞬时跳跃。由此产生的系统增加了一组定时器，触发新测量的到来，并在混合系统框架中进行分析。依靠混合系统的 Lyapunov 工具和饱和条件下的控制设计技术，我们以矩阵不等式的形式提出充分条件，以确保包含对象原点的闭集的区域指数稳定性，即具有保证区域的指数稳定性的吸引力。具体来说，以椭圆集的形式提供了对吸引盆地的明确估计。利用这些条件，提出了一种基于半定规划的设计程序，以设计一个具有最大盆地吸引力的稳定控制器。示例显示了所提出方法的有效性。