- ▪J.P. Hespanha, D. Liberzon, D. Angeli, E.D. Sontag, "Nonlinear norm-observability notions and stability of switched systems", IEEE Trans. Automat. Control, vol. 50, no. 2, pp. 154–168, 2005. pdf
Abstract
This paper proposes several definitions of observability for nonlinear systems and explores relationships among them. These observability properties involve the existence of a bound on the norm of the state in terms of the norms of the output and the input on some time interval. A Lyapunov-like sufficient condition for observability is also obtained. As an application, we prove several variants of LaSalle's stability theorem for switched nonlinear systems. These results are demonstrated to be useful for control design in the presence of switching as well as for developing stability results of Popov type for switched feedback systems.
- ▪W. Desch, H. Logemann, E. P. Ryan, E.D. Sontag, "Meagre functions and asymptotic behaviour of dynamical systems", Nonlinear Anal., vol. 44, no. 8, Ser. A: Theory Methods, pp. 1087–1109, 2001. doipdf
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.