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第12期 顾则全等：一类线性不确定切换系统的鲁棒镇定 .1275. [3]张霄力，刘玉忠，赵军.一类离散系统的渐近稳定性，控制理 [8]顾则全，廖福成，刘贺平，不确定广义系统的保性能控制： 论与应用，2002,19(5)：774 LM1方法.北京科技大学学报，2006,28(1)：93 [4]Narendra K S,Balakrishnan J.A common Lyapunov function for [9]Savkin A V,Skafidas E,Evans R J.Robust output feedback sta- stable LTI systems with commuting A matrices.IEEE Trans Au- bilizability via controller switching Automatica.1999.35:69 tom Control,1994,39(12):2469 [10]JiZ.Wang L.Xie G.New results on the quadratic stabilization [5]Xie D.Wang L.Hao F,et al.Robust stability analysis and con- of switehed linear systems//Proceedings of the 42nd IEEE Con- trol synthesis for discrete time uncertain switched systemsPro ference on Decision and Control.Maui:IEEE Press,2003; ceedings of the 42nd IEEE Conference on Decision and Control. 1657 Maui:IEEE Press,2003:4812 [11]Xie G.Wang L.New results on stabilizability of switched linear [6]Xie D.Wang L.Hao F,et al.An LMI approach to Lagain anal- systems//Proceedings of the 42nd IEEE Conference on Decision ysis and control synthesis of switched systems//IEEE Internation- and Control.Maui:IEEE Press,2003:6265 al Symposium on Computer Aided Control Systems Design. [12]Skafidas E.Evans R J,Savkin A V.et al.Stability results for Taibei:Taiwan Press.2004:350 switched controller systems.Automatica.1999,35(4):553 [7]Daafow J.Riedinger P.lung C.Stability analysis and control [13】张霄力，刘玉忠，赵军.一类切换系统的鲁棒控制·东北大 synthesis for switched systems:A sw itched Lyapunov function 学学报：自然科学版，2000,21(5)：498 approach.IEEE Trans Autom Control,2002.47(11):1883 Robust stabilization for a class of uncertain switched linear systems GU Zequan,LIU Heping,LI Xiaoli),LIAO Fucheng2) 1)Information Engineering School.University of Science and Technology Beijing.Beijing 100083,China 2)Applied Science School.University of Science and Technology Beijing.Beijing 100083.China ABSTRACI Robust stabilization for a class of uncertain switched linear systems whose nominal systems have a common Lyapunov function was considered.With the certain restriction of uncertainty,a kind of robust con- troller of state feedback was constructed by using the completeness condition and common Lyapunov function technique.The closed-loop system still has a common Lyapunov function.The designed controller can guarantee the states of the closed-loop system asymptotically stable at the equilibrium point under an arbitrary switching strategy.Simulation result shows the validity of the designed controller. KEY WORDS switched linear systems;completeness:Lyapunov function:state feedback;robust stabilization［3］ 张霄力刘玉忠赵军．一类离散系统的渐近稳定性．控制理 论与应用200219（5）：774 ［4］ Narendra K SBalakrishnan J．A common Lyapunov function for stable LTI systems with commuting A-matrices．IEEE Trans Autom Control199439（12）：2469 ［5］ Xie DWang LHao Fet al．Robust stability analysis and control synthesis for discrete-time uncertain switched systems∥Proceedings of the 42nd IEEE Conference on Decision and Control． Maui：IEEE Press2003：4812 ［6］ Xie DWang LHao Fet al．An LMI approach to L2gain analysis and control synthesis of switched systems∥IEEE International Symposium on Computer Aided Control Systems Design． Taibei：Taiwan Press2004：350 ［7］ Daafouz JRiedinger PIung C．Stability analysis and control synthesis for switched systems：A switched Lyapunov function approach．IEEE Trans Autom Control200247（11）：1883 ［8］ 顾则全廖福成刘贺平．不确定广义系统的保性能控制： LMI 方法．北京科技大学学报200628（1）：93 ［9］ Savkin A VSkafidas EEvans R J．Robust output feedback stabilizability via controller switching．Automatica199935：69 ［10］ Ji ZWang LXie G．New results on the quadratic stabilization of switched linear systems∥Proceedings of the42nd IEEE Conference on Decision and Control．Maui：IEEE Press2003： 1657 ［11］ Xie GWang L．New results on stabilizability of switched linear systems∥Proceedings of the42nd IEEE Conference on Decision and Control．Maui：IEEE Press2003：6265 ［12］ Skafidas EEvans R JSavkin A Vet al．Stability results for switched controller systems．Automatica199935（4）：553 ［13］ 张霄力刘玉忠赵军．一类切换系统的鲁棒控制．东北大 学学报：自然科学版200021（5）：498 Robust stabilization for a class of uncertain switched linear systems GU Zequan 1）LIU Heping 1）LI Xiaoli 1）LIAO Fucheng 2） 1） Information Engineering SchoolUniversity of Science and Technology BeijingBeijing100083China 2） Applied Science SchoolUniversity of Science and Technology BeijingBeijing100083China ABSTRACT Robust stabilization for a class of uncertain switched linear systems whose nominal systems have a common Lyapunov function was considered．With the certain restriction of uncertaintya kind of robust controller of state feedback was constructed by using the completeness condition and common Lyapunov function technique．The closed-loop system still has a common Lyapunov function．The designed controller can guarantee the states of the closed-loop system asymptotically stable at the equilibrium point under an arbitrary switching strategy．Simulation result shows the validity of the designed controller． KEY WORDS switched linear systems；completeness；Lyapunov function；state feedback；robust stabilization 第12期 顾则全等： 一类线性不确定切换系统的鲁棒镇定 ·1275·