线性离散时滞系统的Gl_2状态反馈控制  

Gl_2 state-feedback control for linear discrete-time systems with time delay

作　　者：张彦虎[1] 颜文俊[1] 赵光宙[1] 

机构地区：[1]浙江大学系统科学与工程系,杭州310027

出　　处：《控制与决策》2007年第4期436-439,444,共5页Control and Decision

基　　金：国家自然科学基金项目(60374028)

摘　　要：研究具有状态时滞的线性离散时不变系统的Gl2控制问题.基于简化的Gl2分析定理,Gl2控制问题被等价转化为H∞控制问题.通过LMI和构造Lyapunov函数,得到了Gl2性能的LMI表述.给出了使得时滞系统稳定且满足给定性能指标的无记忆Gl2状态反馈控制器存在的充分条件和设计方法.当系统具有独立范数有界扰动输入和全结构不确定性时,使用此方法设计得到的Gl2控制器比H∞控制器的保守性更小.算例验证了该方法的有效性.The problem of Gl2 control for discrete-time linear time-invariant systems with time delay in the state is presented, Based on the simplified Gl2 analysis theorem, the Gl2 control problem is equivalently transformed to the H∞ control prolem. The linear matrix inequality （LMI） representation of Gl2 performance for the delayed systems is also derived by using LMI and constructing Lyapunov function. The sufficient condition for the existence of memoryless Gl2 state feedback controller ensuring the stability and a prescribed performance index for the state delay is established. Using the proposed method, the designed Gl2 controller is less conservative than the H∞ controller when the input disturbance is independently norm-bounded and the systems with time delay have full structure uncertainty. A numerical example shows the effectiveness of the result.

关 键 词：LMI Gl2性能 时滞 独立范数有界扰动 全结构不确定性 

分 类 号：TP27[自动化与计算机技术—检测技术与自动化装置]