Previous |  Up |  Next


nonlinear systems; stabilization; passivity; state feedback
A cascade scheme for passivity-based stabilization of a wide class of nonlinear systems is proposed in this paper. Starting from the definitions and basic concepts of passivity-based stabilization via feedback (which are applicable to minimum phase nonlinear systems expressed in their normal forms) a cascade stabilization scheme is proposed for minimum and non-minimum phase nonlinear systems where the constraint of stable zero dynamics imposed by previous stabilization approaches is abandoned. Simulation results of the proposed algorithm are presented to demonstrate its performance.
[1] S. Behtach and S. Sastry: Stabilization of nonlinear systems with uncontrollable linearization. IEEE Trans. Automat. Control 33 (1988) 585–590. MR 0940781
[2] C. I. Byrnes, A. Isidori and J. C. Willems: Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE Trans. Automat. Control 36 (1991), 11, 1228–1240. MR 1130493
[3] D. Cheng and C. Martin: Stabilization of nonlinear systems via designed center manifold. IEEE Trans. Automat. Control 46 (2001), 1372–1383. MR 1853679
[4] C. A. Desoer and M. Vidyasagar: Feedback Systems: Input-Output Properties. Academic Press, New York 1975. MR 0490289
[5] S. Devasia, D. Chen, and B. Paden: Nonlinear inversion based output tracking. IEEE Trans. Automat. Control 41 (1996), 930–942. MR 1398777
[6] S. Devasia and P. Paden: Exact output tracking for nonlinear time-varying system. In: Proc. IEEE Conference on Decision and Control 1994, pp. 2346–2355.
[7] L. Diao and M. Guay: Output feedback stabilization of uncertain non-minimum phase nonlinear systems. In: Proc. 2004 American Control Conference, Boston 2004, ThP13.2.
[8] Z. Ding: Semi-global stabilization of a class of non-minimum phase non-linear output-feedback systems. IEE Proc. Control Theory Appl. 152 (2005), 4, 460–464.
[9] M. A. Duarte-Mermoud, R. Castro-Linares A. and Castillo-Facuse: Adaptive passivity of nonlinear systems using time-varying gains. Dynamics Control 11 (2001), 4, 333–351. MR 1935467
[10] M. A. Duarte-Mermoud, R. Castro-Linares, and A. Castillo-Facuse: Direct passivity of a class of MIMO nonlinear systems using adaptive feedback. Internat. J. Control 75 (2002), 1, 23–33. MR 1878471
[11] A. Duarte-Mermoud and J. C. Travieso: Control of induction motors: An adaptive passivity MIMO perspective. Internat. J. Adaptive Control Signal Process. 17 (2003), 4, 313–332.
[12] D. Hill and P. Moylan: Stability results for nonlinear feedback systems. Automatica 13 (1977), 373–382.
[13] A. Isidori: Nonlinear Control Systems. Third edition. Springer-Verlag, Berlin – Heigelberg – New York 1995. Zbl 0931.93005
[14] A. Isidori: A too1 for semiglobal stabilization of uncertain non-minimum-phase nonlinear system via output feedback. IEEE Trans. Automat. Control 45 (2000), 10, 1817–1827. MR 1795350
[15] P. V. Kokotovic and M. Arcak: Constructive nonlinear control: A historical perspective. Automatica 37 (2001), 637–662. MR 1832954
[16] M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic: Nonlinear and Adaptive Control Design. Wiley, New York 1995.
[17] M. A. Duarte-Mermoud, J. M. Méndez-Miquel, R. Castro-Linares. and A. Castillo-Facuse: Adaptive passivation with time-varying gains of MIMO nonlinear systems. Kybernetes 32 (2003), 9/10, 1342–1368.
[18] K. Narendra and A. Annaswamy: Stable Adaptive Systems. Prentice-Hall, Englewood Cliffs, N.J. 1988.
[19] B. A. Ogunnaike and W. H. Ray: Process Dynamics Modeling and Control. First edition. Oxford – New York 1994.
[20] C. J. Tomlin and S. S. Sastry: Bounded tracking for non-minimum phase system with fast zero dynamics. Internat. J. Control 68 (1998), 819–847. MR 1689727
[21] J. C. Willems: Dissipative dynamical systems Part I: General theory. Arch. Rational Mech. Anal. 45 (1972), 325–351.
[22] J. C. Willems: Dissipative dynamical systems Part II: Linear systems with quadratic supply rates. Arch. Rational Mech. Anal. 45 (1972), 352–393. MR 0527463
[23] R. A. Wright and C. Kravaris: Nonminimum-phase compensation for nonlinear processes. AIChE J. 38 (1992), 26–40. MR 1144842
[24] B. J. Yang and A. J. Calise: Adaptive stabilization for a class of non-affine non-minimum phase systems using neural networks. In: Proc. 2006 American Control Conference, Minneapolis 2006, ThA05.6, pp. 2291–2296.
Partner of
EuDML logo