不确定时延NCS的输出反馈鲁棒H_∞保性能控制

Robust H_∞ Guaranteed Cost Control for Output Feedback Network Control System with Uncertain Time-delay

针对一类具有不确定时延和有限能量外部扰动的网络控制系统,采用Lyapunov和线性矩阵不等式方法,研究了基于输出反馈的鲁棒H_∞保性能网络控制问题。构造一个新的Lyapunov泛函,推导出使得闭环网络控制系统鲁棒稳定,且具有给定H_∞扰动衰减度γ的输出反馈保性能控制器存在的充分条件;通过求解具有约束条件的凸优化问题,给出闭环网络控制系统最优H_∞保性能控制器的设计方法,该方法能在给定扰动衰减度γ的情况下有更小的保性能指标。最后通过YALMIP(一种定义和求解高级优化问题的模化语言)求解数值算例验证了所提出方法的正确性和有效性。

The problem of output feedback robust H∞ guaranteed cost control is studied for a class of networked control systems with uncertain delay and limited energy unknown disturbances based on the Lyapunov and the linear matrix inequality approach. A new Lyapunov functional is proposed, and the sufficient condition for guaranteeing the robust stability of the closed-loop networked control systems and the existence of output feedback guaranteed cost controller is derived. The design method of output feedback optimal H∞ guaranteed cost controller is proposed by solving the convex optimization problem. The designed output feedback guaranteed cost controller has a prescribed H∞ disturbance attenuation γ. This method can have a smaller guaranteed performance indicator in the case of a given disturbance attenuation γ. Finally, a numerical example is presented by YALMIP （a modelling language for advanced modeling and solution of convex and nonconvex optimization problems） to demonstrate the feasibility and validity of the proposed method.