Improved Exponential Stability Criteria for Uncertain Neutral System with Nonlinear Parameter Perturbations

Fang Qiu; Bao-Tong Cui

doi:10.1007/s11633-010-0522-8

November 2010

Article Contents

Fang Qiu and Bao-Tong Cui. Improved Exponential Stability Criteria for Uncertain Neutral System with Nonlinear Parameter Perturbations. International Journal of Automation and Computing, vol. 7, no. 4, pp. 413-418, 2010. doi: 10.1007/s11633-010-0522-8

Cite as: Fang Qiu and Bao-Tong Cui. Improved Exponential Stability Criteria for Uncertain Neutral System with Nonlinear Parameter Perturbations. International Journal of Automation and Computing, vol. 7, no. 4, pp. 413-418, 2010. doi: 10.1007/s11633-010-0522-8

Improved Exponential Stability Criteria for Uncertain Neutral System with Nonlinear Parameter Perturbations

Fang Qiu^{1
,
,},
Bao-Tong Cui²

1.
Department of Mathematics and Information Science, Binzhou University, Binzhou 256603, PRC;
2.
College of Communications and Control Engineering, Jiangnan University, Wuxi 214122, PRC

Author Biography:

Bao-Tong Cui received the Ph.D.
Corresponding author: Fang Qiu received the M.Sc.degree in applied mathematics from Peking University,PRC in 2002.She is now a Ph.D.

Received: 2009-10-10

Fund Project:

supported by Natural Science Foundation of Jiangsu Province of China(No.BK2007016);Scientific Research and Development Program of the Higher Education Institutions of Shandong Province of China(No.J09LG58)

Abstract

This paper investigates the problem of robust exponential stability for neutral systems with time-varying delays and nonlinear perturbations. Based on a novel Lyapunov functional approach and linear matrix inequality technique, a new delay-dependent stability condition is derived. Since the model transformation and bounding techniques for cross terms are avoided, the criteria proposed in this paper are less conservative than some previous approaches by using the free-weighting matrices. One numerical example is presented to illustrate the effectiveness of the proposed results.
- Neutral system,
- time-varying delay,
- exponential stability,
- nonlinear perturbation,
- linear matrix inequality (LMI)

References

[1]	V.B.Kolmanovskii,A.Myshkis.Applied Theory of Func-tional Differential Equations,Netherlands:Kluwer Aca-demic Publishers,1992.
[2]	S.Boyd,L.E.Ghaoui,E.Feron,V.Balakrishnan.Lin-ear Matrix Inequalities in System and Control Theory, Philadelphia,PA,USA:SIAM,1994.
[3]	M.Slemrod,E.F.Infante.Asymptotic stability criteria for linear systems of differential equations of neutral type and their discrete analogues.Journal of Mathematical Analysis and Applications,vol.38,no.2,pp.399-415,1972.
[4]	A.G.Wu,G.R.Duan.On Delay-independent stability cri-teria for linear time-delay systems.International Journal of Automation and Computing,vol.4,no.1,pp.95-100,2007.
[5]	Y.He,Q.G.Wang,L.H.Xie,C.Lin.Further improvement of free-weighting matrices technique for systems with time-varying delay.IEEE Transactions on Automatic Control, vol.52,no.2,pp.293-299,2007.
[6]	Y.He,M.Wu,J.H.She,G.P.Liu.Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopictype uncertainties.IEEE Transactions on Auto-matic Control,vol.49,no.5,pp.828-832,2004.
[7]	Y.He,Q.G.Wang,C.Lin,M.Wu.Augmented Lyapunov functional and delay-dependent stability criteria for neu-tral systems.International Journal of Robust and Nonlinear Control,vol.15,no.18,pp.923-933,2005.
[8]	M.Wu,Y.He,J.H.She.New delay-dependent stabil-ity criteria and stabilizing method for neutral systems. IEEE Transactions on Automatic Control,vol.49,no.12, pp.2266-2271,2004.
[9]	F.E.Haoussi,E.H.Tissir.Robust H_∞controller design for uncertain neutral systems via dynamic observer based out-put.International Journal of Automation and Computing, vol.6,no.2,pp.164-170,2009.
[10]	X.G.Liu,M.Wu,R.Martin,M.L.Tang.Delay-dependent stability analysis for uncertain neutral systems with time-varying delays.Mathematics and Computers in Simulation, vol.75,no.1-2,pp.15-27,2007.
[11]	Z.Zhao,W.Wang,B.Yang.Delay and its time-derivative dependent robust stability of neutral control system. Applied Mathematics and Computation,vol.187,no.2, pp.1326-1332,2007.
[12]	J.H.Park.Novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear pertur-bations.Applied Mathematics and Computation,vol.161, no.2,pp.413-421,2005.
[13]	O.M.Kwon,J.H.Park,S.M.Lee.On stability crite-ria for uncertain delay-di?erential systems of neutral type with time-varying delays.Applied Mathematics and Com-putation,vol.197,no.2,pp.864-873,2008.
[14]	O.M.Kwona,J.H.Park.Exponential stability of uncertain dynamic systems including state delay.Applied Mathemat-ics Letters,vol.19,no.9,pp.901-907,2006.
[15]	S.Y.Xu,J.Lam,M.Y.Zhong.New exponential estimates for time-delay systems.IEEE Transactions on Automatic Control,vol.51,no.9,pp.1501-1506,2006.
[16]	P.L.Liu.Exponential stability for linear time-delay sys-tems with delay dependence.Journal of the Franklin Insti-tute,vol.340,no.6-7,pp.481-488,2003.
[17]	Y.Chen,A.K.Xue,R.Q.Lu,S.S.Zhou.On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations.Nonlinear Analysis:Theory,Methods&Applications,vol.68,no.8, pp.2464-2470,2008.
[18]	Y.Y.Cao,J.Lam.Computation of robust stability bounds for time-delay systems with nonlinear time-varying pertur-bations.International Journal of Systems Science,vol.31, no.3,pp.359-365,2000.
[19]	Q.L.Han.On robust stability for a class of linear systems with time varying delay and nonlinear perturbations.Com-puters&Mathematics with Applications,vol.47,no.8-9, pp.1201-1209,2004.
[20]	Q.L.Han.[J].L.Yu.Robust stability of linear neutral systems with nonlinear parameter perturbations.IEE Proceedings: Control Theory&Applications,vol.151,no.5,pp.539-54.2004,:-
[21]	C.C.Shen,S.M.Zhong.New delay-dependent robust sta-bility criterion for uncertain neutral systems with time-varying delay and nonlinear uncertainties.Chaos,Solitons &Fractals,vol.40,no.5,pp.2277-2285,2009.
[22]	J.H.Zhang,S.Peng,J.Q.Qiu.Robust stability criteria for uncertain neutral system with time delay and nonlin-ear uncertainties.Chaos,Solitons&Fractals,vol.38,no.1, pp.160-167,2008.
[23]	J.K.Hale,S.M.V.Lunel.Introduction to Functional Dif-ferential Equations,Applied Mathematical Sciences,New York,USA:Springer-Verlag,1993.

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1.
沈阳化工大学材料科学与工程学院沈阳 110142

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Improved Exponential Stability Criteria for Uncertain Neutral System with Nonlinear Parameter Perturbations

1. Department of Mathematics and Information Science, Binzhou University, Binzhou 256603, PRC;

2. College of Communications and Control Engineering, Jiangnan University, Wuxi 214122, PRC

Corresponding author: Fang Qiu received the M.Sc.degree in applied mathematics from Peking University,PRC in 2002.She is now a Ph.D.

Received: 2009-10-10

Fund Project:

Key words:

Abstract: This paper investigates the problem of robust exponential stability for neutral systems with time-varying delays and nonlinear perturbations. Based on a novel Lyapunov functional approach and linear matrix inequality technique, a new delay-dependent stability condition is derived. Since the model transformation and bounding techniques for cross terms are avoided, the criteria proposed in this paper are less conservative than some previous approaches by using the free-weighting matrices. One numerical example is presented to illustrate the effectiveness of the proposed results.

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Reference (23)

[1]	V.B.Kolmanovskii,A.Myshkis.Applied Theory of Func-tional Differential Equations,Netherlands:Kluwer Aca-demic Publishers,1992.
[2]	S.Boyd,L.E.Ghaoui,E.Feron,V.Balakrishnan.Lin-ear Matrix Inequalities in System and Control Theory, Philadelphia,PA,USA:SIAM,1994.
[3]	M.Slemrod,E.F.Infante.Asymptotic stability criteria for linear systems of differential equations of neutral type and their discrete analogues.Journal of Mathematical Analysis and Applications,vol.38,no.2,pp.399-415,1972.
[4]	A.G.Wu,G.R.Duan.On Delay-independent stability cri-teria for linear time-delay systems.International Journal of Automation and Computing,vol.4,no.1,pp.95-100,2007.
[5]	Y.He,Q.G.Wang,L.H.Xie,C.Lin.Further improvement of free-weighting matrices technique for systems with time-varying delay.IEEE Transactions on Automatic Control, vol.52,no.2,pp.293-299,2007.
[6]	Y.He,M.Wu,J.H.She,G.P.Liu.Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopictype uncertainties.IEEE Transactions on Auto-matic Control,vol.49,no.5,pp.828-832,2004.
[7]	Y.He,Q.G.Wang,C.Lin,M.Wu.Augmented Lyapunov functional and delay-dependent stability criteria for neu-tral systems.International Journal of Robust and Nonlinear Control,vol.15,no.18,pp.923-933,2005.
[8]	M.Wu,Y.He,J.H.She.New delay-dependent stabil-ity criteria and stabilizing method for neutral systems. IEEE Transactions on Automatic Control,vol.49,no.12, pp.2266-2271,2004.
[9]	F.E.Haoussi,E.H.Tissir.Robust H_∞controller design for uncertain neutral systems via dynamic observer based out-put.International Journal of Automation and Computing, vol.6,no.2,pp.164-170,2009.
[10]	X.G.Liu,M.Wu,R.Martin,M.L.Tang.Delay-dependent stability analysis for uncertain neutral systems with time-varying delays.Mathematics and Computers in Simulation, vol.75,no.1-2,pp.15-27,2007.
[11]	Z.Zhao,W.Wang,B.Yang.Delay and its time-derivative dependent robust stability of neutral control system. Applied Mathematics and Computation,vol.187,no.2, pp.1326-1332,2007.
[12]	J.H.Park.Novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear pertur-bations.Applied Mathematics and Computation,vol.161, no.2,pp.413-421,2005.
[13]	O.M.Kwon,J.H.Park,S.M.Lee.On stability crite-ria for uncertain delay-di?erential systems of neutral type with time-varying delays.Applied Mathematics and Com-putation,vol.197,no.2,pp.864-873,2008.
[14]	O.M.Kwona,J.H.Park.Exponential stability of uncertain dynamic systems including state delay.Applied Mathemat-ics Letters,vol.19,no.9,pp.901-907,2006.
[15]	S.Y.Xu,J.Lam,M.Y.Zhong.New exponential estimates for time-delay systems.IEEE Transactions on Automatic Control,vol.51,no.9,pp.1501-1506,2006.
[16]	P.L.Liu.Exponential stability for linear time-delay sys-tems with delay dependence.Journal of the Franklin Insti-tute,vol.340,no.6-7,pp.481-488,2003.
[17]	Y.Chen,A.K.Xue,R.Q.Lu,S.S.Zhou.On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations.Nonlinear Analysis:Theory,Methods&Applications,vol.68,no.8, pp.2464-2470,2008.
[18]	Y.Y.Cao,J.Lam.Computation of robust stability bounds for time-delay systems with nonlinear time-varying pertur-bations.International Journal of Systems Science,vol.31, no.3,pp.359-365,2000.
[19]	Q.L.Han.On robust stability for a class of linear systems with time varying delay and nonlinear perturbations.Com-puters&Mathematics with Applications,vol.47,no.8-9, pp.1201-1209,2004.
[20]	Q.L.Han.[J].L.Yu.Robust stability of linear neutral systems with nonlinear parameter perturbations.IEE Proceedings: Control Theory&Applications,vol.151,no.5,pp.539-54.2004,:-
[21]	C.C.Shen,S.M.Zhong.New delay-dependent robust sta-bility criterion for uncertain neutral systems with time-varying delay and nonlinear uncertainties.Chaos,Solitons &Fractals,vol.40,no.5,pp.2277-2285,2009.
[22]	J.H.Zhang,S.Peng,J.Q.Qiu.Robust stability criteria for uncertain neutral system with time delay and nonlin-ear uncertainties.Chaos,Solitons&Fractals,vol.38,no.1, pp.160-167,2008.
[23]	J.K.Hale,S.M.V.Lunel.Introduction to Functional Dif-ferential Equations,Applied Mathematical Sciences,New York,USA:Springer-Verlag,1993.

Improved Exponential Stability Criteria for Uncertain Neutral System with Nonlinear Parameter Perturbations

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