Abstract
In this paper, the problem of stability analysis for uncertain dynamic systems with time-varying delays is considered. The parametric uncertainties are assumed to be bounded in magnitude. Based on the Lyapunov stability theory, a new delay-dependent stability criterion for the system is established in terms of linear matrix inequalities, which can be solved easily by various efficient convex optimization algorithms. Two numerical examples are illustrated to show the effectiveness of proposed method.
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Udwadia, F.E., Weber, H.I., Leitmann, G.: Dynamical Systems and Control. Chapman & Hall/CRC, London (2004)
Leitmann, G., Udwadia, F.E., Kryazhimskii, A.V.: Dynamics and Control. CRC Press, Boca Raton (1999)
Hale, J., Lunel, S.M.V.: Introduction to Functional Differential Equations. Springer, New York (1993)
Kolmanovskii, V.B., Myshkis, A.: Applied Theory of Functional Differential Equations. Kluwer Academic, Boston (1992)
Phohomsiri, P., Udwadia, F.E., Von Bremmen, H.: Time-delayed positive velocity feedback control design for active control of structures. J. Eng. Mech. 132, 690–703 (2006)
Udwadia, F.E., Hosseini, M.A.M., Chen, Y.H.: Robust control of uncertain systems with time varying delays in control input. In: Proceedings of the American Control Conference, Albuquerque, New Mexico, pp. 3641–3644 (1997)
Park, J.H., Won, S.: A note on stability of neutral delay-differential systems. J. Franklin Inst. 336, 543–548 (1999)
Park, J.H., Won, S.: Asymptotic stability of neutral systems with multiple delays. J. Optim. Theory Appl. 103, 183–200 (1999)
Nam, P.T., Phat, V.N.: Robust stabilization of linear systems with delayed state and control. J. Optim. Theory Appl. 140, 287–200 (2009)
Park, J.H.: Robust stabilization for dynamic systems with multiple time-varying delays and nonlinear uncertainties. J. Optim. Theory Appl. 108, 155–174 (2001)
Chen, J.D.: Delay-dependent nonfragile H ∞ observer-based control for neutral systems with time delays in the state and control input. J. Optim. Theory Appl. 141, 445–460 (2009)
Kwon, O.M., Park, J.H.: On improved delay-dependent robust control for uncertain time-delay systems. IEEE Trans. Automat. Control 49, 1991–1995 (2004)
Kwon, O.M., Park, J.H.: Matrix inequality approach to novel stability criterion for time delay systems with nonlinear uncertainties. J. Optim. Theory Appl. 126, 643–656 (2005)
Lien, C.H.: Guaranteed cost observer-based controls for a class of uncertain neutral time-delay systems. J. Optim. Theory Appl. 126, 137–156 (2005)
Kwon, O.M., Park, J.H., Lee, S.M.: On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays. Appl. Math. Comput. 197, 864–873 (2008)
Lien, C.H.: Delay-dependent stability criteria for uncertain neutral systems with multiple time-varying delays via LMI approach. IEE Proc., Control Theory Appl. 152, 707–714 (2005)
Niculescu, S.I.: Delay Effects on Stability: A Robust Control Approach. LNCIS, vol. 269. Springer, Berlin (2001)
Park, P.G.: A delay-dependent stability criterion for systems with uncertain linear state-delayed systems. IEEE Trans. Automat. Control 35, 876–877 (1999)
Yue, D., Won, S., Kwon, O.: Delay dependent stability of neutral systems with time delay: an LMI approach. IEE Proc., Control Theory Appl. 150, 23–27 (2003)
Park, J.H., Kwon, O.: On new stability criterion for delay-differential systems of neutral type. Appl. Math. Comput. 162, 627–637 (2005)
Park, P.G., Ko, J.W.: Stability and robust stability for systems with a time-varying delay. Automatica 43, 1855–1858 (2007)
Gouaisbaut, F., Peaucelle, D.: Delay-dependent stability of time delay systems. In: 5th IFAC Symposium on Robust Control Design, Center of Toulouse, France (2006)
Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)
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Kwon, O.M., Park, J.H. & Lee, S.M. An Improved Delay-Dependent Criterion for Asymptotic Stability of Uncertain Dynamic Systems with Time-Varying Delays. J Optim Theory Appl 145, 343–353 (2010). https://doi.org/10.1007/s10957-009-9637-x
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DOI: https://doi.org/10.1007/s10957-009-9637-x