奇异不确定性多时滞系统的二次稳定性与H∞控制

针对奇异不确定性多时滞系统,研究了其二次稳定性及H∞状态反馈控制器的设计.假定其中的不确定性是范数有界的,通过构造改进的Lyapunov泛函,给出了其二次稳定性及H∞状态反馈控制器存在的条件.仅通过求解相应的线性矩阵不等式(linear matrix inequality,LMI)就可得到鲁棒H∞控制器,设计的控制器对所有容许的不确定性不仅使得相应的闭环系统渐进稳定,也能保证闭环系统满足一定的H∞性能指标,达到抑制干扰的效果.最后,用数值算例及仿真验证了所给方法的有效性.

Quadratic stability and H∞ control for the singular uncertain systems with multi-time delay

Focuses on the research of quadratic stabilization and H_ controller design for the singular uncertain systems with multi-time delay. Based on the modified Lyapunov functions, under the assumption that the uncertainty is norm-bounded, an existing conditions of quadratic stabilization and H_ state feedback controller are given. The H_ controller can be obtained by solving the corresponding linear matrix inequality. This controller designed can make the closed-loop systems asymptotically stable, as well as satisfying H_ properties to achieve disturbance attenuation. At last, a numerical example and simulation are presented to illustrate the validity of this approach.