离散线性时滞系统的近周期脉冲镇定

近周期脉冲是一类特殊的脉冲,它与一个标称周期脉冲的误差是一个不确定的时变有界项.本文通过增维方法消除线性系统时滞的影响,构造线性差分包含刻画系统在脉冲时刻的状态,从而利用线性差分包含中蕴含的近周期脉冲信息,构造一个时变Lyapunov函数来进行稳定性分析,得到用线性矩阵不等式表示的带近周期脉冲的离散线性时滞系统的稳定性准则.在此基础上,为离散线性时滞系统分别设计了降阶和全阶近周期脉冲控制器.降阶控制器节省资源,效率高,而全阶控制器适用范围更广.最后,用3个数值算例验证文中方法的有效性.

Stabilization of Discrete-time Linear System with Time Delays via Nearly-periodic Impulses

Nearly-periodic impulse is a class of special type of impulses, the error between which and a nominal periodic impulse is an uncertain time-varying bounded term.The effect of time delays is eliminated from system by means of increment-dimensional method.Then a linear difference inclusion (LDI) is constructed to describe the system states at the impulse instants.A time-varying Lyapunov function is introduced to analyze the stability of system under consideration, which utilizes the information about nearly-periodic impulse contained in the LDI, and a stability criterion is obtained in the form of linear matrix inequalities.Based on the derived stability results, reduced-order and full-order nearly-periodic impulsive controllers are designed for discrete-time linear systems with time-delays, respectively.The former saves system resources and is more efficient, while the latter is more applicable.Three numerical examples are presented to show the effectiveness of the proposed method.