Exponential Stability of Linear Delay Difference Equations with Continuous Time
Tóm tắt
Linear time-varying delay difference equations with continuous time are considered. New criteria for exponential stability are given. Furthermore, an explicit stability bound for equations subject to time-varying perturbations is presented. Some examples are given to illustrate the obtained results.
Tài liệu tham khảo
Melchor-Aguilar, D., Kharitonov, V., Lozano, R.: Stability conditions for integral delay systems. Int. J. Robust Nonlinear Control 20, 1–15 (2010)
Melchor-Aguilar, D.: Exponential stability of linear continuous time difference systems with multiple delays. Syst. Control Lett. 62, 811–818 (2013)
Melchor-Aguilar, D.: Further results on exponential stability of linear continuous time difference systems. Appl. Math. Comput. 219, 10025–10032 (2013)
Courtemanche, M., Keener, J.P., Glass, L.: A delay equation representation of pulse circulation on a ring in excitable media. SIAM J. Appl. Math. 56, 119–142 (1996)
Cruz, M.A., Hale, J.K.: Stability of functional differential equations of neutral type. J. Differ. Equ. 7, 334–355 (1970)
Hale, J.K., Martinez-Amores, P.: Stability in neutral equations. Nonlinear Anal. 1, 161–172 (1977)
Hale, J.K., Lunel, S.M.V.: Introduction to Functional Differential Equations. Springer-Verlag (1993)
Hinrichsen, D., Son, N.K.: Stability radii of positive discrete-time systems under affine parameter perturbations. Int. J. Robust Nonlinear Control 8, 1169–1188 (1988)
Kharitonov, V.L., Melchor-Aguilar, D.: On delay-dependent stability conditions for time-varying systems. Syst. Control Lett. 46, 173–180 (2002)
Li, Z.-Y., Zhou, B., Lin, Z.: On exponential stability of integral delay systems. Am. Control Conf. (ACC) Washington, DC, USA, June, 17–19 (2013)
Michiels, W., Vyhlídal, T.: An eigenvalue based approach for the stabilization of linear time-delay systems of neutral type. Automation 41, 991–998 (2005)
Michiels, W., Vyhlídal, T., Zítek, P., Nijmeijer, H., Henrion, D.: Strong stability of neutral equations with an arbitrary delay dependency structure. SIAM J. Control Optim. 48, 763–786 (2009)
Ngoc, P.H.A., Naito, T., Shin, J.S.: On stability of a class of positive linear functional difference equations. Math. Control Signals Syst. 19, 361–382 (2007)
Ngoc, P.H.A., Hieu, L.T.: New criteria for exponential stability of nonlinear difference systems with time-varying delay. Int. J. Control 86, 1646–1651 (2013)