具有时滞依赖的不确定系统鲁棒H_∞保代价控制

Robust H_∞ guaranteed cost control for the uncertain systems with dependent time-delay

针对一类含有时滞依赖的不确定线性系统,研究了具有鲁棒H∞性能的保代价控制器的设计。假定其中的不确定性是范数有界的和系统的状态是完全可测的,采用基于线性矩阵不等式和构造适当的Lyapunov泛函相结合的方法,给出了一种鲁棒H∞状态反馈保代价控制器的设计,仅通过求解相应的线性矩阵不等式就可得到鲁棒H∞状态反馈保代价控制器,所设计的保代价控制器对所有容许的不确定性不仅使相应的闭环系统渐进稳定,而且能保证闭环系统满足一定的鲁棒H∞保代价性能指标,达到抑制干扰的效果。最后,用数值算例及仿真结果验证了所给方法的可解性和有效性。

The design of robust H∞ guaranteed cost controller was studied for the uncertain systems with dependent time-delay. Based on the proper Lyapunov functions and linear matrix inequality（LMI）, and the assumption that the uncertainty is norm-bounded and the states of the system are available, an approach was put forward to design a state feedback guaranteed cost controllers for all admissible uncertainties, which made the closed-loop systems asymptotically stable, as well as satisfying H∞ guaranteed cost control properties to achieve disturbance attenuation, At last, a numerical example was presented to illustrate the feasibility and validity of this approach.