Integral Input to State Stable systems in cascade

The Integral Input to State Stability (iISS) property is studied in the context of nonlinear time-invariant systems in cascade. Some sufficient conditions for the preservation of the iISS property under a cascade interconnection are presented. These are first given as growth restrictions on the supply functions of the storage function associated with each subsystem and are then expressed as solutions-based requirements. A Lyapunov-based condition guaranteeing that the cascade composed of an iISS system driven by a Globally Asymptotically Stable (GAS) one remains GAS is also provided. We also show that some of these results extend to cascades composed of more than two subsystems.

[1]  Eduardo Sontag.  Remarks on stabilization and input-to-state stability , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[2]  H. Ito,et al.  Explicit solutions to state-dependent scaling problems for interconnected iISS and ISS nonlinear systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[3]  David Angeli,et al.  A characterization of integral input-to-state stability , 2000, IEEE Trans. Autom. Control..

[4]  E. Panteley,et al.  On global uniform asymptotic stability of nonlinear time-varying systems in cascade , 1998 .

[5]  M. Vidyasagar.  Decomposition techniques for large-scale systems with nonadditive interactions: Stability and stabilizability , 1980 .

[6]  H. Ito.  Stability criteria for interconnected iISS systems and ISS systems using scaling of supply rates , 2004, Proceedings of the 2004 American Control Conference.

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

[8]  H. Ito,et al.  Nonlinear Small-Gain Condition Covering iISS Systems: Necessity and Sufficiency from a Lyapunov Perspective , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[9]  David Angeli,et al.  A Unifying Integral ISS Framework for Stability of Nonlinear Cascades , 2001, SIAM J. Control. Optim..

[10]  Eduardo D. Sontag,et al.  An example of a GAS system which can be destabilized by an integrable perturbation , 2003, IEEE Trans. Autom. Control..

[11]  R. Suárez,et al.  Global stabilization of nonlinear cascade systems , 1990 .

[12]  Antonio Loría,et al.  Growth rate conditions for uniform asymptotic stability of cascaded time-varying systems , 2001, Autom..

[13]  João Pedro Hespanha,et al.  Examples of GES systems that can be driven to infinity by arbitrarily small additive decaying exponentials , 2004, IEEE Transactions on Automatic Control.

[14]  Eduardo Sontag,et al.  Changing supply functions in input/state stable systems , 1995, IEEE Trans. Autom. Control..

[15]  David Angeli,et al.  Separation Principles for Input-Output and Integral-Input-to-State Stability , 2004, SIAM J. Control. Optim..

[16]  Eduardo Sontag.  Comments on integral variants of ISS , 1998 .