中文摘要：

研究了一类有时滞环节的离散分段仿射系统的稳定性及其H∞控制器的设计方法。提出了各时滞分段仿射子系统离散时间状态集的椭圆集表示方法,结合Lyapunov意义的稳定约束,以LMIs形式给出了闭环分段时滞仿射系统的稳定充分条件,从而将系统H∞性能指标最小问题转化成LMI的凸约束求解问题。最后,通过仿真实例验证了所提方法的有效性。

英文摘要：

This paper dealt with the problem concerning the stabilization of a discrete-time piecewise affine（PWA） systems with time-delay.An H∞ state feedback controller design was proposed,and the PWA systems described as ellipsoid which was characterized by a set of vector inequalities were presented,thereby the constraint of linear matrix inequalities（LMIs） was released.In terms of LMIs,the time-delay PWA system can be stabilized according to Lyapunov theory.The minimum problem of the H∞ performance index can be cast as a convex optimization problem with LMIs constraints.The simulation results verify the effectiveness of the proposed method.