1. E.P. Ryan and E.D. Sontag. Well-defined steady-state response does not imply CICS. Systems and Control Letters, 55:707-710, 2006. [PDF] [doi:10.1016/j.sysconle.2006.02.001] Keyword(s): nonlinear stability, dynamical systems. Abstract:

   Systems for which each constant input gives rise to a unique globally attracting equilibrium are considered. A counterexample is provided to show that inputs which are only asymptotically constant may not result in states converging to equilibria (failure of the converging-input converging state, or ``CICS'' property).




2. W. Desch, H. Logemann, E. P. Ryan, and E.D. Sontag. Meagre functions and asymptotic behaviour of dynamical systems. Nonlinear Anal., 44(8, Ser. A: Theory Methods):1087-1109, 2001. [PDF] [doi:http://dx.doi.org/10.1016/S0362-546X(99)00323-5] Keyword(s): invariance principle. Abstract:

   A measurable function x from a subset J of R into a metric space X is said to be C-meagre if C is non-empty subset of X and, for every closed subset K of X disjoint from C, the preimage of K under x has finite Lebesgue measure. This concept of meagreness, applied to trajectories, is shown to provide a unifying framework which facilitates a variety of characterizations, extensions or generalizations of diverse facts pertaining to asymptotic behaviour of dynamical systems.

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