Exponential Stability for Uncertain Dynamic Systems with Time-Varying Delays: LMI Optimization Approach
Tóm tắt
In this paper, we consider dynamic systems with uncertainties and time-varying delays. Based on the Lyapunov method and convex optimization approach, a delay-dependent criterion for exponential stability of the system is derived in terms of LMI (linear matrix inequality). In order to solve effectively the LMI convex optimization problem, an interior-point algorithm is utilized in this work. Numerical examples are illustrated to show the effectiveness of our results.
Tài liệu tham khảo
Hale, J., Lune, S.M.V.: Introduction to Functional Differential Equations. Springer, New York (1993)
Kolmanovskii, V.B., Myshkis, A.: Applied Theory of Functional Differential Equation. Kluwer Academic, Boston (1992)
Mori, T.: Criteria for asymptotic stability of linear time-delay systems. IEEE Trans. Autom. Control 30(2), 158–161 (1985)
Mahmoud, M.S., Zribi, M.: H ∞ controllers for time-delay systems using linear matrix inequalities. J. Optim. Theory Appl. 100(1), 89–122 (1999)
Park, J.H., Won, S.: Asymptotic stability of neutral systems with multiple delays. J. Optim. Theory Appl. 103(1), 183–200 (1999)
Park, J.H., Won, S.: A note on stability of neutral delay-differential systems. J. Frankl. Inst. 336, 543–548 (1999)
Park, J.H.: Robust stabilization for dynamic systems with multiple time-varying delays and nonlinear uncertainties. J. Optim. Theory Appl. 108(1), 155–174 (2001)
Yue, D., Won, S., Kwon, O.: Delay dependent stability of neutral systems with time delay: an LMI approach. IEE Proc. Control Theory Appl. 150(1), 23–27 (2003)
Yue, D., Won, S., Kwon, O.: Design of delay dependent robust controller for uncertain systems with time-varying delay. In: 15th Triennial World Congress of the International Federation of Automatic Control, Barcelona, Spain, July 21, 2002
Park, J.H.: On dynamic output feedback guaranteed cost control of uncertain discrete-delay systems: an LMI optimization approach. J. Optim. Theory Appl. 121(1), 147–162 (2004)
He, Y., Wu, M., She, J.H., Liu, G.P.: Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. Syst. Control Lett. 51, 57–65 (2004)
Kwon, O.M., Park, J.H.: Improved delay-dependent robust control for uncertain time-delay systems. IEEE Trans. Autom. Control 49(11), 1991–1995 (2004)
Lien, C.H.: Guaranteed cost observer-based controls for a class of uncertain neutral time-delay systems. J. Optim. Theory Appl. 126(1), 137–156 (2005)
Zhang, X.M., Wu, M., She, J.H., He, Y.: Delay-dependent stabilization of linear systems with time-varying state and input delays. Automatica 41, 1405–1412 (2005)
Kwon, O., Park, J.H.: Matrix inequality approach to novel stability criterion for time-delay systems with nonlinear uncertainties. J. Optim. Theory Appl. 126(3), 643–656 (2005)
Lien, C.H.: Stability and stabilization criteria for a class of uncertain neutral systems with time-varying delays. J. Optim. Theory Appl. 124(3), 637–657 (2005)
Park, J.H.: Convex optimization approach to dynamic output feedback control for delay differential systems of neutral type. J. Optim. Theory Appl. 127(2) (2005)
Park, J.H., Choi, K.: Guaranteed cost control of uncertain nonlinear neutral systems via memory state feedback. Chaos Solitons Fractals 24, 183–190 (2005)
Park, J.H.: Design of dynamic controller for neutral differential systems with delay in control input. Chaos Solitons Fractals 23, 503–509 (2005)
Park, J.H., Kwon, O.: On new stability criterion for delay-differential systems of neutral type. Appl. Math. Comput. 162, 627–637 (2005)
Mondié, S., Kharitonov, V.L.: Exponential estimates for retarded time-delay systems: an LMI approach. IEEE Trans. Autom. Control 50(2), 268–273 (2005)
Kwon, O.M., Park, J.H.: Robust H ∞ filtering for uncertain time-delay systems: matrix inequality approach. J. Optim. Theory Appl. 129(2), 309–324 (2006)
Kwon, O.M., Park, J.H., Lee, S.M., Won, S.C.: LMI optimization approach to observer-based controller design of uncertain time-delay systems via delayed feedback. J. Optim. Theory Appl. 128(1), 103–117 (2006)
Kwon, O.M., Park, J.H.: Decentralized guaranteed cost control for uncertain large-scale systems using delayed feedback: LMI optimization approach. J. Optim. Theory Appl. 129(3), 391–414 (2006)
Kwon, O.M., Park, J.H.: Robust stabilization of uncertain systems with delays in control input. Appl. Math. Comput. 172, 1067–1077 (2006)
Kwon, O.M., Park, J.H.: Exponential stability of uncertain dynamic systems including state delay. Appl. Math. Lett. 19, 901–907 (2006)
Xu, S., Lam, J., Zhong, M.: New exponential estimates for time-delay systems. IEEE Trans. Autom. Control 51(9), 1501–1505 (2006)
Gu, K.: An integral inequality in the stability of time-delay systems. In: IEEE Conference on Decision and Control, Sydney, Australia, 2000
Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in Systems and Control Theory. Studies in Applied Mathematics, vol. 15. SIAM, Philadelphia (1994)
Gahinet, P., Nemirovski, A., Laub, A., Chilali, M.: LMI Control Toolbox User’s Guide. The Mathworks, Natick (1995)