Stability Analysis of Unified Chaotic Systems via Switching Control
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- 英文论文题名：Stability Analysis of Unified Chaotic Systems via Switching Control
- 论文作者：Changchun Sun ; Xin Jing
- 英文论文作者：Changchun Sun ; Xin Jing ; Shenyang Jianzhu University
- 年：2017
- 作者机构：Shenyang Jianzhu University;
- 英文论文关键词：switched unified chaotic systems ; common quadratic Lyapunov function ; switching control ; chaotic attractor
- 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：O231;O415.5
- 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：5
- 文件大小：185k
- 原文格式：D
- 会议级别：全国
摘要
The problem on the existence of a common quadratic Lyapunov function for switched unified chaotic systems is investigated in this paper. Switched unified chaotic systems with a varying parameter are constructed. A sufficient condition on the existence of a common quadratic Lyapunov function is derived in view of the solution to a group of matrix inequalities. By designing linear state feedback controllers, the controlled switched unified chaotic systems can be asymptotically stable via arbitrary switching. Finally, a random numerical example and its simulations illustrate the effectiveness of the switching control approach.
The problem on the existence of a common quadratic Lyapunov function for switched unified chaotic systems is investigated in this paper. Switched unified chaotic systems with a varying parameter are constructed. A sufficient condition on the existence of a common quadratic Lyapunov function is derived in view of the solution to a group of matrix inequalities. By designing linear state feedback controllers, the controlled switched unified chaotic systems can be asymptotically stable via arbitrary switching. Finally, a random numerical example and its simulations illustrate the effectiveness of the switching control approach.
The problem on the existence of a common quadratic Lyapunov function for switched unified chaotic systems is investigated in this paper. Switched unified chaotic systems with a varying parameter are constructed. A sufficient condition on the existence of a common quadratic Lyapunov function is derived in view of the solution to a group of matrix inequalities. By designing linear state feedback controllers, the controlled switched unified chaotic systems can be asymptotically stable via arbitrary switching. Finally, a random numerical example and its simulations illustrate the effectiveness of the switching control approach.
引文
[1]D.Liberzon and A.S.Morse,Basic problems in stability and design of switched systems,IEEE Control Systems Magazine,19(5):59–70,1999.
[2]K.S.Narendra and J.Balakrishnan,A common Lyapunov function for stable LTI systems with commuting A-matrices.IEEE Transactions on Automatic Control,39(12):2469–2471,1994.
[3]R.N.Shorten and K.S.Narendra,On common quadratic Lyapunov functions for pairs of stable LTI systems whose system matrices are in companion form,IEEE Transactions on Automatic Control,48(4):618–621,2003.
[4]C.Sun,B.Fang and W.Huang,Existence of a common quadratic Lyapunov function for discrete switched linear systems with m stable subsystems,IET Control Theory&Applications,5(3):535–537,2011.
[5]C.C.Sun,B.Fang and W.H.Huang,Global control of chaotic systems based on linear state feedback,Acta Physica Sinica,60(11),110503,2011.
[6]E.N.Lorenz,Deterministic nonperiodic flow,Journal of the Atmospheric Sciences,20(2):130–141,1963.
[7]G.R.Chen and T.Ueta,Yet another chaotic attractor,International Journal Bifurcation and Chaos,9(7):1465–1466,1999.
[8]J.H.Lüand G.R.Chen,A new chaotic attractor coined,International Journal of Bifurcation and Chaos,12(3):659–661,2002.
[9]J.H.Lü,G.R.Chen,D.Z.Cheng,and S.Celikovsky,Bridge the gap between the Lorenz system and the Chen system,International Journal Bifurcation and Chaos,12(12):2917–2926,2002.
[10]T.S.Zhou and G.R.Chen,A simple smooth chaotic system with a 3-layer attractor,International Journal Bifurcation and Chaos,14(5):1795–1799,2004.
[11]X.Wang and G.R.Chen,Constructing a chaotic system with any number of equilibria,Nonlinear Dynamics,71(3):429–436,2013.
[12]C.C.Sun,E.L.Zhao,and Q.C.Xu,Generation of a novel spherical chaotic attractor from a new three-dimensional system,Chinese Physics B,23(5):050505,2014.
[2]K.S.Narendra and J.Balakrishnan,A common Lyapunov function for stable LTI systems with commuting A-matrices.IEEE Transactions on Automatic Control,39(12):2469–2471,1994.
[3]R.N.Shorten and K.S.Narendra,On common quadratic Lyapunov functions for pairs of stable LTI systems whose system matrices are in companion form,IEEE Transactions on Automatic Control,48(4):618–621,2003.
[4]C.Sun,B.Fang and W.Huang,Existence of a common quadratic Lyapunov function for discrete switched linear systems with m stable subsystems,IET Control Theory&Applications,5(3):535–537,2011.
[5]C.C.Sun,B.Fang and W.H.Huang,Global control of chaotic systems based on linear state feedback,Acta Physica Sinica,60(11),110503,2011.
[6]E.N.Lorenz,Deterministic nonperiodic flow,Journal of the Atmospheric Sciences,20(2):130–141,1963.
[7]G.R.Chen and T.Ueta,Yet another chaotic attractor,International Journal Bifurcation and Chaos,9(7):1465–1466,1999.
[8]J.H.Lüand G.R.Chen,A new chaotic attractor coined,International Journal of Bifurcation and Chaos,12(3):659–661,2002.
[9]J.H.Lü,G.R.Chen,D.Z.Cheng,and S.Celikovsky,Bridge the gap between the Lorenz system and the Chen system,International Journal Bifurcation and Chaos,12(12):2917–2926,2002.
[10]T.S.Zhou and G.R.Chen,A simple smooth chaotic system with a 3-layer attractor,International Journal Bifurcation and Chaos,14(5):1795–1799,2004.
[11]X.Wang and G.R.Chen,Constructing a chaotic system with any number of equilibria,Nonlinear Dynamics,71(3):429–436,2013.
[12]C.C.Sun,E.L.Zhao,and Q.C.Xu,Generation of a novel spherical chaotic attractor from a new three-dimensional system,Chinese Physics B,23(5):050505,2014.