Interconnected nonlinear systems, local and global stabilization

A family of interconnected nonlinear systems including partially linear systems is studied. No assumption on the stability of each uncontrolled subsystem is imposed but asymptotic stabilizability for each of them is assumed. The objective of this work is the state feedback stabilization of the origin of such composite systems. Local and global results are derived using simple techniques such as coordinate and feedback transformations.

[1]  J. Carr.  Applications of Centre Manifold Theory , 1981 .

[2]  L. Praly,et al.  Adding an integration and global asymptotic stabilization of feedforward systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[3]  P. Kokotovic,et al.  Global stabilization of partially linear composite systems , 1990 .

[4]  Rogelio Lozano,et al.  Passivity and global stabilization of cascaded nonlinear systems , 1992 .

[5]  D. Aeyels.  Stabilization of a class of nonlinear systems by a smooth feedback control , 1985 .

[6]  A. Teel.  A nonlinear small gain theorem for the analysis of control systems with saturation , 1996, IEEE Trans. Autom. Control..

[7]  A. Teel.  Semi-global stabilization of minimum phase nonlinear systems in special normal forms , 1992 .

[8]  P. Kokotovic,et al.  Global stabilization of an enlarged class of cascade nonlinear systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[9]  Eduardo Sontag.  A universal construction of Artstein's theorem on nonlinear stabilization , 1989 .

[10]  H. Sussmann.  Limitations on the stabilizability of globally-minimum-phase systems , 1990 .

[11]  W. Respondek,et al.  Feedback Equivalence of Planar Systems and Stabilizability , 1990 .

[12]  Eduardo Sontag,et al.  On characterizations of the input-to-state stability property , 1995 .

[13]  P. Kokotovic,et al.  Constructive Lyapunov stabilization of nonlinear cascade systems , 1996, IEEE Trans. Autom. Control..

[14]  Julio H. Braslavsky,et al.  Global and semi-global stabilizability in certain cascade nonlinear systems , 1996, IEEE Trans. Autom. Control..

[15]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[16]  L. Praly,et al.  Adding integrations, saturated controls, and stabilization for feedforward systems , 1996, IEEE Trans. Autom. Control..

[17]  Zongli Lin,et al.  Semi-global stabilization of partially linear composite systems via feedback of the state of the linear part , 1993 .

[18]  Frédéric Mazenc,et al.  Stabilization of feedforward systems approximated by a non-linear chain of integrators , 1997 .