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Articles

An extended-observer approach to robust stabilisation of linear differential-algebraic systems

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Pages 181-193 | Received 29 Mar 2018, Accepted 22 Oct 2018, Published online: 13 Nov 2018

References

  • Banaszuk, A., Kociecki, M., & Przy Iuski, K. (1990). The disturbance decoupling problem for implicit linear discrete-time systems. SIAM Journal on Control and Optimization, 28(6), 1270–1293. doi: 10.1137/0328068
  • Benner, P. (2011). Partial stabilization of descriptor systems using spectral projectors. Lecture Notes in Electrical Engineering, 80, 53–76.
  • Berger, T. (2013). On differential-algebraic control systems. Ph.D. thesis. Technische Universit at Ilmenau.
  • Berger, T. (2014). Zero dynamics and stabilization for linear DAEs. In S. Schöps, A. Bartel, M. Günther, E. J. W. ter Maten, and P. C. Müller (Eds.), Progress in differential-algebraic equations, differential-algebraic equations forum (pp. 21–45). Berlin, Heidelberg: Springer-Verlag.
  • Berger, T. (2016). Zero dynamics and funnel control of general linear differential-algebraic systems. ESAIM: Control, Optimization and Calculus of Variations, 22(2), 371–403. doi: 10.1051/cocv/2015010
  • Berger, T. (2017). Disturbance decoupling by behavioral feedback for linear differential algebraic systems. Automatica, 80, 272–283. doi: 10.1016/j.automatica.2017.01.012
  • Berger, T., & Reis, T. (2017). Observers and dynamic controllers for linear differential-algebraic systems. SIAM Journal on Control and Optimization, 55(6), 3564–3591. doi: 10.1137/15M1035355
  • Bruni, C., Delli Priscoli, F., Koch, G., & Marchetti, I. (2010). Resource management in network dynamics: An optimal approach to the admission control problem. Computers & Mathematics with Applications, 59(1), 305–318. doi: 10.1016/j.camwa.2009.01.046
  • Dai, L. (1989). Singular control systems. Berlin: Springer-Verlag.
  • Darouach, M., & Boutayeb, M. (1995). Design of observers for descriptor systems. IEEE Transactions on Automatic Control, 40(7), 1323–1327. doi: 10.1109/9.400467
  • Di Giorgio, A., Pietrabissa, A., Delli Priscoli, F., & Isidori, A. (2018). Robust output regulation for a class of linear differential-algebraic systems. IEEE Control Systems Letters, 2(3), 477–482. doi: 10.1109/LCSYS.2018.2841805
  • Duan, G. R., Liu, G. P., & Thompson, S. (2000). Disturbance decoupling in descriptor systems via output feedback – a parametric eigenstructure assignment approach. Proceedings of the 39th IEEE Conference on Decision and Control (Vol. 4, pp. 3660–3665).
  • Eich-Soellner, E., & Fuhrer, C. (1998). Numerical methods in multibody dynamics. Stuttgart: Teubner.
  • Freidovich, L. B., & Khalil, H. K. (2008). Performance recovery of feedback-linearization-based designs. IEEE Transactions on Automatic Control, 53(10), 2324–2334. doi: 10.1109/TAC.2008.2006821
  • Han, J. Q. (1995). A class of extended state observers for uncertain systems. Control and Decision, 10, 85–88.
  • Hill, D., & Mareels, I. (1990). Stability theory for differential-algebraic systems with application to power systems. IEEE Transactions on Circuits and Systems, 37, 1416–1423. doi: 10.1109/31.62415
  • Hou, M., & Müller, P. C. (1999). Observer design for descriptor systems. IEEE Transactions on Automatic Control, 44(1), 164–169. doi: 10.1109/9.739112
  • Isidori, A. (2016). Lectures in feedback design for multivariable systems. Basel: Springer Verlag.
  • Jiang, Z. P., & Praly, L. (1998). Semiglobal stabilization in the presence of minimum-phase dynamic input uncertainties. Proc. of IFAC Symposium on Nonlinear Control Systems Design (pp. 4).
  • Khalil, H. K. (2002). Nonlinear systems (3rd ed.). Upper Saddle River, NJ: Prentice Hall.
  • Kumar, A., & Daoutidis, P. (1998). Control of nonlinear differential algebraic equation systems: an overview. In: R. Berber and C. Kravaris, (Eds.), Nonlinear Model Based Process Control. NATO ASI Series (Series E: Applied Sciences) (pp. 353). Dordrecht: Springer.
  • Kumar, A., & Daoutidis, P. (1999). Control of nonlinear differential algebraic equation systems with applications to chemical processes. Vol. 397 of Chapman Hall/CRC Res. Notes Math). Boca Raton, FL: Chapman and Hall.
  • Lebret, G. (1994). Structural solution of the disturbance decoupling problem for implicit linear discrete-time systems. Circuits Systems Signal Process, 13(2-3), 311–327. doi: 10.1007/BF01188113
  • Lin, W., & Dai, L. (1996). Solutions to the output regulation problem of linear singular systems. Automatica, 32, 1713–1718. doi: 10.1016/S0005-1098(96)80008-2
  • Liu, X., & Ho, D. W. C. (2004). Stabilization of non-linear differential-algebraic equation systems. International Journal of Control, 77(7), 671–684. doi: 10.1080/00207170410001715013
  • Osorio-Gordillo, G., Darouach, M., Astorga-Zaragoza, C., & Boutat-Baddas, L. (2016). New dynamical observers design for linear descriptor systems. IET Control Theory and Applications, 10(17), 2223–2232. doi: 10.1049/iet-cta.2016.0431
  • Pang, S., Huang, J., & Bai, Y. (2005, February). Robust output regulation of singular nonlinear systems via a nonlinear internal model. IEEE Transactions on Automatic Control, 50(2), 222–228. doi: 10.1109/TAC.2004.841934
  • Riaza, R. (2008). Differential-algebraic systems: Analytical aspects and circuit applications. Singapore: World Scientific.
  • Riaza, R. (2013). DAEs in circuit modelling: A survey. In A. Ilchmann and T. Reis, (Eds.), Surveys in Differential-Algebraic Equations I. Springer Science & Business Media.
  • Varga, A. (1995). On stabilization methods of descriptor systems. Systems & Control Letters, 24(2), 133–138. doi: 10.1016/0167-6911(94)00017-P
  • Venkatasubramanian, V., Schattler, H., & Zaborsky, J. (1995). Dynamics of large constrained nonlinear systems – a taxonomy theory. Proceedings of the IEEE, 83(11), 1530–1561. doi: 10.1109/5.481633
  • Wang, L., Isidori, A., & Su, H. (2015). Output feedback stabilization of nonlinear MIMO systems having uncertain high-frequency gain matrix. Systems & Control Letters, 83, 1–8. doi: 10.1016/j.sysconle.2015.06.001
  • Wang, Y., Zhu, S., & Cheng, Z. (2004). Disturbance decoupling for singular systems. In: 2004 43rd IEEE Conference on Decision and Control (Vol 3, pp. 2632–2637).
  • Xu, S., Dooren, P. V., Stefan, R., & Lam, J. (2002). Robust stability and stabilization for singular systems with state delay and parameter uncertainty. IEEE Transactions on Automatic Control, 47(7), 1122–1128. doi: 10.1109/TAC.2002.800651
  • Zimmer, G., & Meier, J. (1997). On observing nonlinear descriptor systems. Systems & Control Letters, 32, 43–48. doi: 10.1016/S0167-6911(97)00054-6

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