Global uniform input-to-state stabilization of large-scale interconnections of MIMO generalized triangular form switched systems

We solve the problem of global uniform input-to-state stabilization with respect to external disturbance signals for a class of large-scale interconnected nonlinear switched systems. The overall system is composed of switched subsystems each of which has the nonlinear MIMO generalized triangular form, which (in contrast to strict-feedback form) has non-invertible input–output maps. The switching signal is an arbitrary unknown piecewise constant function and the feedback constructed does not depend on the switching signal.

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

[2]  Kok Kiong Tan,et al.  Nonlinear adaptive control of interconnected systems using neural networks , 2006, IEEE Transactions on Neural Networks.

[3]  Mariesa L. Crow,et al.  Decentralized control of large scale interconnected systems using adaptive neural network-based dynamic surface control , 2009, 2009 International Joint Conference on Neural Networks.

[4]  Jun Zhao,et al.  Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings , 2010, Autom..

[5]  J. Coron,et al.  Adding an integrator for the stabilization problem , 1991 .

[6]  S. Fomin,et al.  Elements of the Theory of Functions and Functional Analysis , 1961 .

[7]  A. Annaswamy,et al.  Adaptive control of nonlinear systems with a triangular structure , 1994, IEEE Trans. Autom. Control..

[8]  Daizhan Cheng,et al.  ON NONUNIFORM AND SEMI-UNIFORM INPUT-TO-STATE STABILITY FOR TIME VARYING SYSTEMS , 2005 .

[9]  Zhong-Ping Jiang,et al.  Small-gain theorem for ISS systems and applications , 1994, Math. Control. Signals Syst..

[10]  Wei Lin,et al.  Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems , 2000 .

[11]  I. Kanellakopoulos,et al.  Adaptive nonlinear control without overparametrization , 1992 .

[12]  H. Nijmeijer,et al.  Equivalence of nonlinear systems to triangular form: the singular case , 1996 .

[13]  David J. Bell,et al.  Algebraic and Geometric Methods in Nonlinear Control Theory , 2011 .

[14]  Petar V. Kokotovic,et al.  Systematic design of adaptive controllers for feedback linearizable systems , 1991 .

[15]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[16]  J. Tsinias.  A theorem on global stabilization of nonlinear systems by linear feedback , 1991 .

[17]  I. Kolmanovsky,et al.  Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[18]  Shuzhi Sam Ge,et al.  Adaptive neural control for a class of switched nonlinear systems , 2009, Syst. Control. Lett..

[19]  Zhong-Ping Jiang,et al.  A combined backstepping and small-gain approach to adaptive output feedback control , 1999, Autom..

[20]  Zhong-Ping Jiang,et al.  Design of Robust Adaptive Controllers for Nonlinear Systems with Dynamic Uncertainties , 1998, Autom..

[21]  Jenq-Lang Wu,et al.  Stabilizing controllers design for switched nonlinear systems in strict-feedback form , 2009, Autom..

[22]  J. Tsinias,et al.  Explicit formulas of feedback stabilizers for a class of triangular systems with uncontrollable linearization , 1999 .

[23]  V. I. Korobov,et al.  Global properties of the triangular systems in the singular case , 2008 .

[24]  Arthur J. Krener,et al.  Backstepping design with local optimality matching , 2001, IEEE Trans. Autom. Control..

[25]  Sheng Zhang,et al.  Backstepping Stabilization for a class of SISO Switched Nonlinear Systems with trigonal structure , 2007 .

[26]  Shuzhi Sam Ge,et al.  Global Stabilization of the Generalized MIMO Triangular Systems With Singular Input-Output Links , 2009, IEEE Transactions on Automatic Control.

[27]  J. L. Mancilla-Aguilar,et al.  On converse Lyapunov theorems for ISS and iISS switched nonlinear systems , 2001 .

[28]  W. Respondek.  Global Aspects of Linearization, Equivalence to Polynomial Forms and Decomposition of Nonlinear Control Systems , 1986 .

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

[30]  Fabian R. Wirth,et al.  An ISS small gain theorem for general networks , 2007, Math. Control. Signals Syst..

[31]  Robert Shorten,et al.  Stability Criteria for Switched and Hybrid Systems , 2007, SIAM Rev..

[32]  Wei Lin,et al.  On p-normal forms of nonlinear systems , 2003, IEEE Trans. Autom. Control..

[33]  Eduardo Aranda-Bricaire,et al.  Constructive nonsmooth stabilization of triangular systems , 1999 .

[34]  Sergej Celikovský,et al.  Local stabilization and controllability of a class of non-triangular nonlinear systems , 2000, IEEE Trans. Autom. Control..

[35]  John Tsinias,et al.  Partial-state global stabilization for general triangular systems , 1995 .