Xin, H.; Gan, D.; Qiu, J. Stability analysis of linear dynamical systems with saturation nonlinearities and a short time delay. (English) Zbl 1220.93065 Phys. Lett., A 372, No. 22, 3999-4009 (2008). Summary: A class of linear dynamical systems subject to saturation nonlinearities and a short time delay were approximated by singular perturbation dynamical systems with saturation nonlinearities based on the notion of Pade approximation. The stability region of the approximate systems was proved to be decomposed and a convex linear matrix inequality (LMI) optimization model was introduced to estimate the decomposed stability region with least degree of conservativeness. Cited in 2 Documents MSC: 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory 34D15 Singular perturbations of ordinary differential equations 37F15 Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems 41A21 Padé approximation Keywords:saturation nonlinearity; singular perturbation dynamical systems; time delay; Padé approximation PDFBibTeX XMLCite \textit{H. Xin} et al., Phys. Lett., A 372, No. 22, 3999--4009 (2008; Zbl 1220.93065) Full Text: DOI References: [1] Hu, T.; Lin, Z., Control Systems with Actuator Saturation: Analysis and Design (2001), Birkhäuser: Birkhäuser Boston · Zbl 1061.93003 [2] Gan, D.; Xin, H.; Qiu, J.; Han, Z., Sci. China Ser. E, 50, 1 (2007) [3] Xin, H.; Gan, D.; Chung, T. S.; Qiu, J. J., Electric Power Syst. Res., 77, 1284 (2007) [4] Cao, Y. Y.; Lin, Z.; Hu, T., IEEE Trans. Circuits Syst. I: Fundam. Theory Appl., 49, 233 (2002) [5] Wu, H.; Tsakalis, K.; Heydt, G., IEEE Trans. Power Syst., 19, 1935 (2004) [6] Xi, Z.; Feng, G.; Cheng, D.; Lu, Q., IEEE Trans. Control Syst. T, 11, 539 (2003) [7] Han, Q., Phys. Lett. A, 360, 563 (2007) [8] Tissir, E.; Hmamed, A., Int. J. Syst. Sci., 23, 615 (1992) [9] Wang, Z.; Hu, H., Nonlinear Dynam., 18, 275 (1999) [10] Chen, J.; Latchman, H. A., IEEE Trans. Automat. Control, 40, 1640 (1995) [11] Chou, J.; Horng, I.; Chen, B. S., Int. J. Control, 49, 961 (1989) [12] Niculescu, S.; Dion, J.; Duqard, L., IEEE Trans. Automat. Control, 41, 742 (1996) [13] Oucheriah, S., IEEE Trans. Circuits Syst. I: Fundam. Theory Appl., 43, 1012 (1996) [14] Tarbouriech, S.; Peres, G.; Queinnec, I., IEE P-Contr. Theory Appl., 149, 387 (2002) [15] Ni, H.; Heydt, G. T.; Mili, L., IEEE Trans. Power Syst., 17, 1123 (2002) [16] George, A.; Baker, J.; Graves-Morris, P., Pade Approximants (1996), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0923.41001 [17] Philipp, L. D.; Mahmood, A.; Philipp, B. L., IEEE Trans. Circuits Syst. I: Fundam. Theory Appl., 46, 637 (1999) [18] Lam, J., Int. J. Control, 57, 377 (1993) [19] Knospe, C. R.; Roozbehani, M., IEEE Trans. Automat. Control, 51, 1271 (2006) [20] Khalil, H. K., Nonlinear Systems (1996), Prentice Hall: Prentice Hall New Jersey · Zbl 0626.34052 [21] Noble, B.; James, W. D., Applied Linear Algebra (1977), Prentice Hall: Prentice Hall New Jersey · Zbl 0413.15002 [22] Kokotovic, P. V.; Khalil, H. K.; O’Reilly, J., Singular Perturbation Methods in Control: Analysis and Design (1986), Academic Press: Academic Press London · Zbl 0646.93001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.