具容许状态反馈PritchardSalamon系统的小时滞鲁棒稳定性(英文)  

Robustness with Respect to Small Delays for Exponential Stabilityof Pritchard-Salamon Systems with Admissible State Feedback

作　　者：刘艳[1] 蒋卫生[1] 黄发伦[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2004年第3期665-667,共3页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(10301025)

摘　　要：It has been observed that for many stable feedback control systems, the introduction of arbitrarily small delays into the loop causes instability. Therefore, robustness of stablility with respect to small delays is of great importance. The authors study the robustness with respect to small delays for exponential stability of Pritchard-Salamon systems with admissible state feedback, i.e. the exponential stability of the following systems are equivalent:x(t)=S(t)x0+∫toS(t-s)BFx(s)dsu(t)=Fx(t),x0∈V,t≥0andx(t)=S(t)x0+∫toS(t-s)BFx(s-r)dsu(t)=Fx(t-r),x0∈V,t≥0and obtain a number of necessary and sufficient conditions, particularly, frequency domain characterization for robustness with respect to small delays for exponential stability.It has been observed that for many stable feedback control systems, the introduction of arbitrarily small delays into the loop causes instability. Therefore, robustness of stablility with respect to small delays is of great importance. The authors study the robustness with respect to small delays for exponential stability of Pritchard-Salamon systems with admissible state feedback, i.e. the exponential stability of the following systems are equivalent:x(t)=S(t)x0+∫toS(t-s)BFx(s)dsu(t)=Fx(t),x0∈V,t≥0andx(t)=S(t)x0+∫toS(t-s)BFx(s-r)dsu(t)=Fx(t-r),x0∈V,t≥0and obtain a number of necessary and sufficient conditions, particularly, frequency domain characterization for robustness with respect to small delays for exponential stability.

关 键 词：容许状态反馈 PRITCHARD-SALAMON系统 小时滞鲁棒稳定性 质数稳定性 C0半群 

分 类 号：O231[理学—运筹学与控制论]