Passivity Based Stabilization of Non-Minimum Phase Nonlinear Systems

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]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[2]  A.J. Calise,et al.  Adaptive stabilization for a class of non-affine non-minimum phase systems using neural networks , 2006, 2006 American Control Conference.

[3]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[4]  Alberto Isidori,et al.  A tool for semi-global stabilization of uncertain non-minimum-phase nonlinear systems via output feedback , 2000, IEEE Trans. Autom. Control..

[5]  M. Guay,et al.  Output feedback stabilization of uncertain non-minimum phase nonlinear systems , 2004, Proceedings of the 2004 American Control Conference.

[7]  B. Paden,et al.  Nonlinear inversion-based output tracking , 1996, IEEE Trans. Autom. Control..

[8]  B. Paden,et al.  Exact output tracking for nonlinear time-varying systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[9]  Murat Arcak,et al.  Constructive nonlinear control: a historical perspective , 2001, Autom..

[10]  S. Sastry,et al.  Stabilization of nonlinear systems with uncontrollable linearization , 1988 .

[11]  Daizhan Cheng,et al.  Stabilization of nonlinear systems via designed center manifold , 2001, IEEE Trans. Autom. Control..

[12]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[13]  R. A. Wright,et al.  Nonminimum‐phase compensation for nonlinear processes , 1992 .

[14]  S. Shankar Sastry,et al.  Bounded tracking for non-minimum phase nonlinear systems with fast zero dynamics , 1997 .

[15]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[16]  Alberto Isidori,et al.  Nonlinear control systems: an introduction (2nd ed.) , 1989 .

[17]  David J. Hill,et al.  Stability results for nonlinear feedback systems , 1977, Autom..

[18]  Manuel A. Duarte-Mermoud,et al.  Control of induction motors: an adaptive passivity MIMO perspective , 2003 .

[19]  Rafael Castro-Linares,et al.  Direct passivity of a class of MIMO non-linear systems using adaptive feedback , 2002 .

[20]  Rafael Castro-Linares,et al.  Adaptive passivation with time‐varying gains of mimo nonlinear systems , 2003 .

[21]  A. Castillo-Facuse,et al.  Adaptive Passivity of Nonlinear Systems Using Time-Varying Gains , 2001 .

[22]  Anuradha M. Annaswamy,et al.  Stable Adaptive Systems , 1989 .

[23]  J. Willems.  Dissipative dynamical systems Part II: Linear systems with quadratic supply rates , 1972 .

[24]  A. Isidori,et al.  Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems , 1991 .