1. M. Malisoff, M. Krichman, and E.D. Sontag. Global stabilization for systems evolving on manifolds. Journal of Dynamical and Control Systems, 12:161-184, 2006. [PDF] Keyword(s): nonlinear stability, nonlinear control, feedback stabilization. Abstract:

   This paper shows that any globally asymptotically controllable system on any smooth manifold can be globally stabilized by a state feedback. Since discontinuous feedbacks are allowed, solutions are understood in the ``sample and hold'' sense introduced by Clarke-Ledyaev-Sontag-Subbotin (CLSS). This work generalizes the CLSS Theorem, which is the special case of our result for systems on Euclidean space. We apply our result to the input-to-state stabilization of systems on manifolds relative to actuator errors, under small observation noise.




2. E.D. Sontag and M. Krichman. An example of a GAS system which can be destabilized by an integrable perturbation. IEEE Trans. Automat. Control, 48(6):1046-1049, 2003. [PDF] Keyword(s): nonlinear stability. Abstract:

   A construction is given of a globally asymptotically stable time-invariant system which can be destabilized by some integrable perturbation. Besides its intrinsic interest, this serves to provide counterexamples to an open question regarding Lyapunov functions.




3. M. Krichman and E.D. Sontag. Characterizations of detectability notions in terms of discontinuous dissipation functions. Internat. J. Control, 75(12):882-900, 2002. [PDF] Keyword(s): input to state stability, detectability, input to output stability, detectability. Abstract:

   We consider a new Lyapunov-type characterization of detectability for nonlinear systems without controls, in terms of lower-semicontinuous (not necessarily smooth, or even continuous) dissipation functions, and prove its equivalence to the GASMO (global asymptotic stability modulo outputs) and UOSS (uniform output-to-state stability) properties studied in previous work. The result is then extended to provide a construction of a discontinuous dissipation function characterization of the IOSS (input-to-state stability) property for systems with controls. This paper complements a recent result on smooth Lyapunov characterizations of IOSS. The utility of non-smooth Lyapunov characterizations is illustrated by application to a well-known transistor network example.




4. M. Krichman, E.D. Sontag, and Y. Wang. Input-output-to-state stability. SIAM J. Control Optim., 39(6):1874-1928, 2001. [PDF] [doi:http://dx.doi.org/10.1137/S0363012999365352] Keyword(s): input to state stability. Abstract:

   This work explores Lyapunov characterizations of the input-output-to-state stability (IOSS) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zero-detectability property used in the linear case. The main contribution of this work is to establish a complete equivalence between the input-output-to-state stability property and the existence of a certain type of smooth Lyapunov function. As corollaries, one shows the existence of "norm-estimators", and obtains characterizations of nonlinear detectability in terms of relative stability and of finite-energy estimates.

1. M. Krichman, E.D. Sontag, and Y. Wang. Lyapunov characterizations of input-ouput-to-state stability. In Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999, pages 2070-2075, 1999. Keyword(s): input to state stability, ISS, detectability.



2. M. Krichman and E.D. Sontag. A version of a converse Lyapunov theorem for input-output to state stability. In Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998, pages 4121-4126, 1998. Keyword(s): input to state stability.

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