基于LMI的奇异不确定时滞系统鲁棒保成本控制

针对一类奇异不确定时滞系统的鲁棒保成本控制，假定其中的不确定性是范数有界，采用基于线性矩阵不等式（LMI）和构造适当的Lyapunov泛函相结合的方法，给出了系统的鲁棒保成本状态反馈控制器存在的条件。通过求解相应的线性矩阵不等式就可得到鲁棒保成本控制，所设计的保成本控制器对所有容许的不确定性不仅使得相应的闭环系统达到二次稳定，也能保证闭环成本函数不超过一个确定的界。通过数值算例及仿真验证了所给方法的有效性。

Robust guaranteed cost control based on LMI for the singular uncertain systems with time-delay

This paper focuses on the design of robust guaranteed cost controller for the singular uncertain systems with time-delay. Based on the LMI and proper Lyapunov functions, under the assumption that the uncertainty is norm-bounded, the existing conditions of the guaranteed cost controllers is given. The guaranteed cost controllers can be obtained by solving the linear matrix inequality, which makes the closedloop systems quadratic stable for all admissible uncertainties, as well as guarantying the cost is bounded in a limitation. At last, a numerical example and simulation are presented to illustrate the validity of this approach.