Global Exponential Stability of Switched Systems

V. Filipovic

doi:10.3879/j.issn.1000-0887.2011.09.011

Volume 32 Issue 9

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V. Filipovic. Global Exponential Stability of Switched Systems[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1118-1126. doi: 10.3879/j.issn.1000-0887.2011.09.011

Citation:

V. Filipovic. Global Exponential Stability of Switched Systems[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1118-1126. doi: 10.3879/j.issn.1000-0887.2011.09.011

Citation:

V. Filipovic. Global Exponential Stability of Switched Systems[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1118-1126. doi: 10.3879/j.issn.1000-0887.2011.09.011

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Global Exponential Stability of Switched Systems

doi: 10.3879/j.issn.1000-0887.2011.09.011

V. Filipovic

Faculty of Mechanical Engineering, University of Kragujevac, Dositejeva 19, Kraljevo 36000, Serbia

Received Date: 2011-02-09
Rev Recd Date: 2011-05-01
Publish Date: 2011-09-15

Abstract

Abstract

A method for stability analysis of deterministic switched systems was proposed.Two motivational examples were introduced (nonholonomic system and constrained pendulum).The finite collection of models consists of nonlinear models and a switching sequence was arbitrary.It was supposed that there was no jump in the state at switching instants and there was no Zeno behavior,i.e.there was finite number of switches on every bounded interval.For analysis of deterministic switched systems,the multiple Liapunov functions were used and global exponential stability was proved.The exponentially stable equilibrium of systems is relevant for practice because such systems are robust to perturbations.
- switching systems,
- multiple Liapunov functions,
- global exponential stability

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References(24)

References

[1]	Tabuda P. Verification and Control of Hybrid Systems, a Symbolic Approach[M]. Berlin: Springer, 2009.
[2]	Liberzon D. Switching in Systems and Control[M]. Berlin: Springer, 2003.
[3]	Sun Z, Ge S. Switched Linear Systems, Control and Design[M]. Berlin: Springer, 2005.
[4]	Brockett R W. Asymptotic stability and feedback stabilization[C]Brockett R W, Millman R S, Susmann H J. Differential Geometric Control Theory. Boston: Birkhauser, 1983: 181-191.
[5]	Cortes J. Discontinuous dynamical systems[J]. IEEE Control Systems Magazine, 2008, 25(1): 36-73.
[6]	Lin H, Antsaklis P J. Stability and stabilizability of switched linear systems: a survey of recent results[J]. IEEE Transactions on Automatic Control, 2009, 54(2): 308-322. doi: 10.1109/TAC.2008.2012009
[7]	Chatterjee D, Liberzon D. Stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple Liapunov function[J]. SIAM Journal on Control and Optimization, 2006, 45(1): 174-206. doi: 10.1137/040619429
[8]	Geromel J C, Colaneri P. Stability and stabilization of continuous-time switched linear systems[J]. SIAM Journal on Control and Optimization, 2006, 45(5): 1915-1930. doi: 10.1137/050646366
[9]	Artstein Z, Romen J. On stabilization of switched linear systems[J]. Systems and Control Letters, 2008, 57(11): 919-926. doi: 10.1016/j.sysconle.2008.05.001
[10]	Santarelli K R, Dahleh M A. Comparison between a switching controller and two LTI controllers for a class of LTI plants[J]. International Journal of Robust and Nonlinear Control, 2009, 19(2): 185-217. doi: 10.1002/rnc.1308
[11]	Filipovic V Z. Hybrid control of systems with input delay[C]Praha, Czech Republic, CD IFAC World Congress, 2005.
[12]	Filipovic V Z. Switching control in the presence of constraints and unmodeled dynamics[C]Aschemann H. New Approaches in Automation and Robotics. I-Tech, Vienna, 2008: 227-238.
[13]	Filipovic V Z, Nedic N. Stability if switched stochastic nonlinear systems[C]Mulder M. Air Traffic Control. SCYO, Vienna, 2010: 23-38.
[14]	Branicky M S. Multiple Liapunov functions and other analysis tools for switched and hybrid systems[J].IEEE Transactions on Automatic Control, 1998, 43(4): 475-482. doi: 10.1109/9.664150
[15]	Guan Z, Hill D, Shen X. On hybrid impulsive and switching systems and application to nonlinear control[J].IEEE Transactions on Automatic Control, 2005, 50(7): 1058-1062. doi: 10.1109/TAC.2005.851462
[16]	Li Z, Soh Y, Wen C. Switched and Impulsive Systems[M]. Berlin: Springer, 2005.
[17]	V·柯维克, M·维什柯维克, D·狄加瑞克, A·阿伯拉达维克.非线性约束下非完整系统的平衡稳定性[J].应用数学和力学, 2010, 31(6): 722-730.(Cˇovic＇ V, Veskovic＇ M, Djuric＇ D, Obradovic＇ A. On the stability of equilibria of nonholonomic systems with nonlinear constraints[J].Applied Mathematics and Mechanics(English Edition), 2010, 31(6): 751-760.) doi: 10.1007/s10483-010-1309-7
[18]	吴凡，耿志勇. 非完整性多体编队运动的一种无源化控制方法[J].应用数学和力学, 2010, 31(1): 26-34.(WU Fan, GENG Zhi-yong. Formation control for nonholonomic agents using passivity techniques[J].Applied Mathematics and Mechanics(English Edition), 2010, 31(1): 27-36.) doi: 10.1007/s10483-010-0104-x
[19]	Sastry S. Nonlinear Systems Analysis, Stability and Control[M]. Berlin: Springer, 1999.
[20]	Van der Schaft A, Schumacher H. An Introduction to Hybrid Dinamical Systems[M]. Berlin: Springer, 2000.
[21]	Morse A S. Supervisory control of families of linear set-point controllers, part 1: exact matching[J]. IEEE Transactions on Automatic Control, 1996, 41(10): 1413-1431. doi: 10.1109/9.539424
[22]	Decarlo R A, Branicky M S, Pettersson S, Lennartson B. Perspectives and results on the stability and stabilizability of hybrid systems[J]. Proceedings of the IEEE, 2000, 88(7): 1069-1082. doi: 10.1109/5.871309
[23]	Isidori A. Nonlinear Control Systems Ⅱ[M].Berlin: Springer, 1999.
[24]	Vidyasagar M. Nonlinear Systems Analysis[M].Philadelphia: SIAM, 2002.