Composite Homogeneous Parameter Dependent Quadratic Lyapunov Functions
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- 英文论文题名：Composite Homogeneous Parameter Dependent Quadratic Lyapunov Functions
- 论文作者：Guochen Pang ; Zhong Xiang ; Feng Zhao
- 英文论文作者：Guochen Pang ; Zhong Xiang ; Feng Zhao ; College of Mechanical Engineering ; Linyi University ; School of mathematical science ; Liaocheng University
- 年：2017
- 作者机构：College of Mechanical Engineering, Linyi University;School of mathematical science, Liaocheng University;
- 英文论文关键词：Homogeneous polynomial functions ; Contractively invariance ; Saturating actuator ; Quadratic Lyapunov functions ; Domain of attraction
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O174
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：348k
- 原文格式：D
- 会议级别：全国
摘要
This paper presents a new type of Lyapunov function which is called composite homogeneous parameter dependent quadratic Lyapunov function. By using this function, a condition is derived in terms of an auxiliary feedback matrix for determining if a given convex hull is an estimation of attractive region for a system under a saturated linear feedback. Most of the cases, the shape of attractive region is irregular. So, using simple ellipsoid to estimate the attractive region will bring conservativeness. However, if we use the complex polyhedron to estimate attractive region, the polyhedron is obviously more closer to attractive region than the simple ellipsoid. Along this direction, we get this polyhedron by constructing the level set of composite homogeneous parameter dependent quadratic Lyapunov function. Simulation results show the features of the proposed design the composite homogeneous parameter dependent quadratic Lyapunov function brings about.
This paper presents a new type of Lyapunov function which is called composite homogeneous parameter dependent quadratic Lyapunov function. By using this function, a condition is derived in terms of an auxiliary feedback matrix for determining if a given convex hull is an estimation of attractive region for a system under a saturated linear feedback. Most of the cases, the shape of attractive region is irregular. So, using simple ellipsoid to estimate the attractive region will bring conservativeness. However, if we use the complex polyhedron to estimate attractive region, the polyhedron is obviously more closer to attractive region than the simple ellipsoid. Along this direction, we get this polyhedron by constructing the level set of composite homogeneous parameter dependent quadratic Lyapunov function. Simulation results show the features of the proposed design the composite homogeneous parameter dependent quadratic Lyapunov function brings about.
This paper presents a new type of Lyapunov function which is called composite homogeneous parameter dependent quadratic Lyapunov function. By using this function, a condition is derived in terms of an auxiliary feedback matrix for determining if a given convex hull is an estimation of attractive region for a system under a saturated linear feedback. Most of the cases, the shape of attractive region is irregular. So, using simple ellipsoid to estimate the attractive region will bring conservativeness. However, if we use the complex polyhedron to estimate attractive region, the polyhedron is obviously more closer to attractive region than the simple ellipsoid. Along this direction, we get this polyhedron by constructing the level set of composite homogeneous parameter dependent quadratic Lyapunov function. Simulation results show the features of the proposed design the composite homogeneous parameter dependent quadratic Lyapunov function brings about.
引文
[1]Y.Chen,S.Fei,K.Zhang,Z.Fu,Control synthesis of discretetime switched linear systems with input saturation based on minimum dwell time approach,Circuits,Systems,and Signal Processing,31(2),779-795,(2012)
[2]G.Chesi,A.Tesi,A.Garulli,A.Vicino Homogneous Polynomial Forms for Robustness Analysis of Uncertain Systems Springer-Verlag:Berlin Heidelberg,(2009)
[3]T.Hu,Z.Lin,Control Systems With Actuator Saturation:Analysis and Design MA:Birkh¨auser:Boston,(2001)
[4]T.Hu,Z.Lin,Composite Quadratic Lyaounov Functions for Constrained Control System,IEEE Transactions on Automatic Control,48(3),440-450(2003)
[5]T.Hu,Z.Lin,Ben M.Chen,An analysis and design method for linear systems subject to actuator saturation and disturbance,Automatica,38(2),351-359,(2002)
[6]S.Ma,EL-Kébir Boukas,Stability and H∞control for discrete-time singular systems subject to actuator saturation,Proceedings of the American Control Conference,(2009),pp.1244-1249
[7]Y.chen,S.Fen,K.Zhang,Improved asymptotic stability conditions for neural networks with discrete and distributed delays,International Journal of Computer Mathematics,89(15),1938-1951,(2012)
[8]L.Lu,Z.Lin,A switching Anti-windup Design Using Multiple Lyapunov Functions,IEEE Transactions On Automatic Control,55(1),142-148,(2010)
[9]L.Lu,Z.Lin,Design of a Nolinear Anti-Windup Gain by Using a Composite Quadratic Lyapunov Function,IEEE Transaction On Automatic Control,56(12),2997-3001,(2011)
[10]Y.Li,Z.Lin,Improvements to the linear differential inclusion approach to stability analysis of linear systems with saturated linear feedback,Automatica,49(3),821-828,(2013)
[11]G.Chesi,Establishing tightness in robust H-infinity analysis via homogeneous parameter-dependent Lyapunov functions,Automatica,43(11),1992-1995,(2007)
[12]G.Chesi,A.Garulli,A.Tesi,A.Vicino,Characterizing the solution set of polynomial systems in terms of homogeneous forms:an LMI approach,Int.Journal of Robust and Nonlinear Control,13(13),1239-1257,(2003)
[13]G.Chesi,A.Garulli,A.Tesi,A.Vicino,Parameter-dependent homogeneous Lyapunov functions for robust stability of linear time-varying systems,Proceedings of the 43rd IEEE Confessor on Decision and Control.(2004),pp.4095-4100
[14]G.Chesi,A.Garulli,A.Tesi,A.Vicino,Robust analysis of LFR systems through homogeneous polynomial Lyapunov functions,IEEE Transactions on Automatic Control,49(7),1211-1216,(2004)
[15]G.Chesi,A.Garulli,A.Tesi,A.Vicino,Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems:an LMI approach,IEEE Transactions on Automatic Control,50(3),365-370,(2005)
[16]G.Chesi,A.Tesi,A.Vicino,R.Genesio,An LMI approach to constrained optimization with homogeneous forms,Systems and Control Letters,42(1),11-19,(2001)
[17]Y.Fujisaki,R.Sakuwa,Estimation of asymptotic stability regions via homogeneous polynomial Lyapunov functions,International Journal of Control,79(6),617-623,(2006)
[2]G.Chesi,A.Tesi,A.Garulli,A.Vicino Homogneous Polynomial Forms for Robustness Analysis of Uncertain Systems Springer-Verlag:Berlin Heidelberg,(2009)
[3]T.Hu,Z.Lin,Control Systems With Actuator Saturation:Analysis and Design MA:Birkh¨auser:Boston,(2001)
[4]T.Hu,Z.Lin,Composite Quadratic Lyaounov Functions for Constrained Control System,IEEE Transactions on Automatic Control,48(3),440-450(2003)
[5]T.Hu,Z.Lin,Ben M.Chen,An analysis and design method for linear systems subject to actuator saturation and disturbance,Automatica,38(2),351-359,(2002)
[6]S.Ma,EL-Kébir Boukas,Stability and H∞control for discrete-time singular systems subject to actuator saturation,Proceedings of the American Control Conference,(2009),pp.1244-1249
[7]Y.chen,S.Fen,K.Zhang,Improved asymptotic stability conditions for neural networks with discrete and distributed delays,International Journal of Computer Mathematics,89(15),1938-1951,(2012)
[8]L.Lu,Z.Lin,A switching Anti-windup Design Using Multiple Lyapunov Functions,IEEE Transactions On Automatic Control,55(1),142-148,(2010)
[9]L.Lu,Z.Lin,Design of a Nolinear Anti-Windup Gain by Using a Composite Quadratic Lyapunov Function,IEEE Transaction On Automatic Control,56(12),2997-3001,(2011)
[10]Y.Li,Z.Lin,Improvements to the linear differential inclusion approach to stability analysis of linear systems with saturated linear feedback,Automatica,49(3),821-828,(2013)
[11]G.Chesi,Establishing tightness in robust H-infinity analysis via homogeneous parameter-dependent Lyapunov functions,Automatica,43(11),1992-1995,(2007)
[12]G.Chesi,A.Garulli,A.Tesi,A.Vicino,Characterizing the solution set of polynomial systems in terms of homogeneous forms:an LMI approach,Int.Journal of Robust and Nonlinear Control,13(13),1239-1257,(2003)
[13]G.Chesi,A.Garulli,A.Tesi,A.Vicino,Parameter-dependent homogeneous Lyapunov functions for robust stability of linear time-varying systems,Proceedings of the 43rd IEEE Confessor on Decision and Control.(2004),pp.4095-4100
[14]G.Chesi,A.Garulli,A.Tesi,A.Vicino,Robust analysis of LFR systems through homogeneous polynomial Lyapunov functions,IEEE Transactions on Automatic Control,49(7),1211-1216,(2004)
[15]G.Chesi,A.Garulli,A.Tesi,A.Vicino,Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems:an LMI approach,IEEE Transactions on Automatic Control,50(3),365-370,(2005)
[16]G.Chesi,A.Tesi,A.Vicino,R.Genesio,An LMI approach to constrained optimization with homogeneous forms,Systems and Control Letters,42(1),11-19,(2001)
[17]Y.Fujisaki,R.Sakuwa,Estimation of asymptotic stability regions via homogeneous polynomial Lyapunov functions,International Journal of Control,79(6),617-623,(2006)