IEEE/CAA Journal of Automatica Sinica
Citation:  Pierluigi Di Franco, Giordano Scarciotti and Alessandro Astolfi, "Stability of Nonlinear DifferentialAlgebraic Systems Via Additive Identity," IEEE/CAA J. Autom. Sinica, vol. 7, no. 4, pp. 929941, July 2020. doi: 10.1109/JAS.2020.1003219 
[1] 
W. Blajer, “Index of differentialalgebraic equations governing the dynamics of constrained mechanical systems,” Appl. Math. Model., vol. 16, no. 2, pp. 70–77, Feb. 1992. doi: 10.1016/0307904X(92)90083F

[2] 
O. Khatib, “A unified approach for motion and force control of robot manipulators: The operational space formulation,” IEEE J. Rob. Autom., vol. 3, no. 1, pp. 43–53, Feb. 1987. doi: 10.1109/JRA.1987.1087068

[3] 
A. Kumar and P. Daoutidis, “Control of nonlinear differential algebraic equation systems: An overview,” in Nonlinear Model Based Process Control, R. Berber and C. Kravaris, Eds. Dordrecht, Netherlands: Springer, 1998, pp. 311–344.

[4] 
R. Riaza, DifferentialAlgebraic Systems: Analytical Aspects and Circuit Applications. London, UK: World Scientific, 2008.

[5] 
T. Fliegner, H. Nijmeijer, and Ü. Kotta, “Some aspects of nonlinear discretetime descriptor systems in economics,” in Predictability and Nonlinear Modelling in Natural Sciences and Economics, J. Grasman and G. van Straten, Eds. Dordrecht, Netherlands: Springer, 1994, pp. 581–590.

[6] 
P. Fritzson, Principles of ObjectOriented Modeling and Simulation With Modelica 2.1. Piscataway, USA: IEEE Press, 2004.

[7] 
M. Arnold, “DAE aspects of multibody system dynamics,” in Surveys in DifferentialAlgebraic Equations IV, A. Ilchmann and T. Reis, Eds, Cham, Germany: Springer, 2017.

[8] 
P. Di Franco, G. Scarciotti, and A. Astolfi, “A globally stable algorithm for the integration of highindex differentialalgebraic systems,” IEEE Trans. Autom. Control, vol. 65, no. 5, pp. 2107–2122, May 2020. doi: 10.1109/TAC.2019.2939638

[9] 
T. Berger, “On observers for nonlinear differentialalgebraic systems,” IEEE Trans. Autom. Control, vol. 64, no. 5, pp. 2150–2157, May 2019. doi: 10.1109/TAC.2018.2866438

[10] 
J. C. Arceo, M. Sánchez, V. EstradaManzo, and M. Bernal, “Convex stability analysis of nonlinear singular systems via linear matrix inequalities,” IEEE Trans. Autom. Control, vol. 64, no. 4, pp. 1740–1745, Apr. 2019. doi: 10.1109/TAC.2018.2854651

[11] 
V. Mehrmann, Index Concepts for DifferentialAlgebraic Equations. Berlin Heidelberg, Germany: Springer, 2015, pp. 676–681.

[12] 
L. Y. Dai, Singular Control Systems. Berlin, Heidelberg, Germany: SpringerVerlag, 1989.

[13] 
N. H. McClamroch, “Feedback stabilization of control systems described by a class of nonlinear differentialalgebraic equations,” Syst. Control Lett., vol. 15, no. 1, pp. 53–60, Jul. 1990. doi: 10.1016/01676911(90)90044U

[14] 
A. Kumar and P. Daoutidis, “Feedback control of nonlinear differentialalgebraicequation systems,” AIChE J., vol. 41, no. 3, pp. 619–636, Mar. 1995. doi: 10.1002/aic.690410319

[15] 
T. N. Chang and E. J. Davison, “Decentralized control of descriptor systems,” IEEE Trans. Autom. Control, vol. 46, no. 10, pp. 1589–1595, Oct. 2001. doi: 10.1109/9.956054

[16] 
J. Åslund and E. Frisk, “An observer for nonlinear differentialalgebraic systems,” Automatica, vol. 42, no. 6, pp. 959–965, Jun. 2006. doi: 10.1016/j.automatica.2006.01.026

[17] 
H. S. Wu and K. Mizukami, “Lyapunov stability theory and robust control of uncertain descriptor systems,” Int. J. Syst. Sci., vol. 26, no. 10, pp. 1981–1991, Oct. 1995. doi: 10.1080/00207729508929149

[18] 
P. G. Wang and J. Zhang, “Stability of solutions for nonlinear singular systems with delay,” Appl. Math. Lett., vol. 25, no. 10, pp. 1291–1295, Oct. 2012. doi: 10.1016/j.aml.2011.11.029

[19] 
D. F. Coutinho, A. S. Bazanella, A. Trofino, and A. S. Silva, “Stability analysis and control of a class of differentialalgebraic nonlinear systems,” Int. J. Robust Nonlinear Control, vol. 14, no. 16, pp. 1301–1326, Nov. 2004. doi: 10.1002/rnc.950

[20] 
K. Takaba, N. Morihira, and T. Katayama, “H_{∞} control for descriptor systems: A Jspectral factorization approach,” in Proc. 33rd IEEE Conf. Decision and Control, Lake Buena Vista, USA, 1994, pp. 2251–2256.

[21] 
I. Masubuchi, Y. Kamitane, A. Ohara, and N. Suda, “H _{∞}
control for descriptor systems: A matrix inequalities approach,” Automatica, vol. 33, no. 4, pp. 669–673, Apr. 1997. doi: 10.1016/S00051098(96)001938

[22] 
H. S. Wang, C. F. Yung, and F. R. Chang, “H _{∞} control for nonlinear descriptor systems,” IEEE Trans. Automatic Control, vol. 47, no. 11, pp. 1919–1925, Nov. 2002.

[23] 
L. Y. Sun and Y. Z. Wang, “An undecomposed approach to control design for a class of nonlinear descriptor systems,” Int. J. Robust Nonlinear Control, vol. 23, no. 6, pp. 695–708, Apr. 2013. doi: 10.1002/rnc.2790

[24] 
C. W. Gear, “Differentialalgebraic equation index transformations,” SIAM J. Sci. Stat. Comput., vol. 9, no. 1, pp. 39–47, Jan. 1988. doi: 10.1137/0909004

[25] 
P. Di Franco, G. Scarciotti, and A. Astolfi, “A note on the stability of nonlinear differentialalgebraic systems,” IFACPapersOnLine, vol. 50, no. 1, pp. 7421–7426, Jul. 2017. doi: 10.1016/j.ifacol.2017.08.1501

[26] 
P. Di Franco, G. Scarciotti, and A. Astolfi, “A disturbance attenuation approach for the control of differentialalgebraic systems,” in Proc. IEEE Conf. Decision and Control, Miami Beach, FL, USA, 2018, pp. 4695–4700.

[27] 
P. Kunkel and V. Mehrmann, DifferentialAlgebraic Equations: Analysis and Numerical Solution. Zurich, Switzerland: European Mathematical Society, 2006.

[28] 
D. C. Tarraf and H. H. Asada, “On the nature and stability of differentialalgebraic systems,” in Proc. American Control Conf., Anchorage, USA, 2002, pp. 3546–3551.

[29] 
P. Di Franco, G. Scarciotti, and A. Astolfi, “On the stability of constrained mechanical systems,” in Proc. IEEE 56th Annu. Conf. Decision and Control, Melbourne, Australia, 2017, pp. 3170–3174.

[30] 
P. Di Franco, G. Scarciotti, and A. Astolfi, “Stabilization of differentialalgebraic systems with Lipschitz nonlinearities via feedback decomposition,” in Proc. 18th European Control Conf., Naples, Italy, 2019.

[31] 
A. Rapaport and A. Astolfi, “Practical L_{2} disturbance attenuation for nonlinear systems,” Automatica, vol. 38, no. 1, pp. 139–145, Jan. 2002. doi: 10.1016/S00051098(01)001765

[32] 
J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “Statespace solutions to standard H_{2} and H_{∞}control problems,” IEEE Trans. Autom. Control, vol. 34, no. 8, pp. 831–847, Aug. 1989. doi: 10.1109/9.29425

[33] 
J. Nestruev, Smooth Manifolds and Observables. New York, USA: Springer, 2003.

[34] 
M. D. S. Aliyu and E. K. Boukas, “H_{∞} filtering for nonlinear singular systems,” IEEE Trans. Circuits Syst. I:Regular Pap., vol. 59, no. 10, pp. 2395–2404, Oct. 2012. doi: 10.1109/TCSI.2012.2189038

[35] 
J. Sjöoberg, K. Fujimoto, and T. Glad, “Model reduction of nonlinear differentialalgebraic equations,” IFAC Proc., vol. 40, no. 12, pp. 176–181, 2007. doi: 10.3182/200708223ZA2920.00030

[36] 
A. Rapaport and A. Astolfi, “A remark on the stability of interconnected nonlinear systems,” IEEE Trans. Autom. Control, vol. 49, no. 1, pp. 120–124, Jan. 2004. doi: 10.1109/TAC.2003.821407

[37] 
A. Isidori, Nonlinear Control Systems II, E. D. Sontag and M. Thoma, Eds. London, UK: Springer, 1995.

[38] 
J. LaSalle, “Some extensions of Liapunov’s second method,” IRE Trans. Circuit Theory, vol. 7, no. 4, pp. 520–527, Dec. 1960. doi: 10.1109/TCT.1960.1086720

[39] 
C. W. Gear, B. Leimkuhler, and G. K. Gupta, “Automatic integration of EulerLagrange equations with constraints,” J. Comput. Appl. Math., vol. 1213, pp. 77–90, May 1985. doi: 10.1016/03770427(85)900081

[40] 
C. Führer and B. J. Leimkuhler, “Numerical solution of differentialalgebraic equations for constrained mechanical motion,” Numerische Mathematik, vol. 59, no. 1, pp. 55–69, Dec. 1991. doi: 10.1007/BF01385770

[41] 
D. Koenig, “Observer design for unknown input nonlinear descriptor systems via convex optimization,” IEEE Trans. Autom. Control, vol. 51, no. 6, pp. 1047–1052, Jun. 2006. doi: 10.1109/TAC.2006.876807

[42] 
L. N. Zhou, C. Y. Yang, and Q. L. Zhang, “Observers for descriptor systems with sloperestricted nonlinearities,” Int. J. Autom. Comput., vol. 7, no. 4, pp. 472–478, Nov. 2010. doi: 10.1007/s1163301005291

[43] 
M. K. Gupta, N. K. Tomar, and S. Bhaumik, “Observer design for descriptor systems with Lipschitz nonlinearities: An LMI approach,” Nonlinear Dyn. Syst. Theory, vol. 14, no. 3, pp. 291–301, Jan. 2014.

[44] 
M. Abbaszadeh and H. J. Marquez, “A generalized framework for robust nonlinear H_{∞} filtering of Lipschitz descriptor systems with parametric and nonlinear uncertainties,” Automatica, vol. 48, no. 5, pp. 894–900, May 2012. doi: 10.1016/j.automatica.2012.02.033

[45] 
W. W. Hager, “Updating the inverse of a matrix,” SIAM Rev., vol. 31, no. 2, pp. 221–239, 1989. doi: 10.1137/1031049

[46] 
H. K. Khalil, Nonlinear Systems. Upper Saddle River, USA: Prentice Hall, 1996.
