- ▪E.D. Sontag, "Input to state stability: Basic concepts and results", In Nonlinear and Optimal Control Theory, pp. 163–220, 2007. pdf
Abstract
This expository presentation, prepared for a summer course, addresses the precise formulation of questions of robustness with respect to disturbances, using the paradigm of input to state stability. It provides an intuitive and informal presentation of the main concepts.
- ▪M. Krichman, E.D. Sontag, "Characterizations of detectability notions in terms of discontinuous dissipation functions", Internat. J. Control, vol. 75, no. 12, pp. 882–900, 2002. pdf
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.
- ▪M. Krichman, E.D. Sontag, Y. Wang, "Lyapunov characterizations of input-ouput-to-state stability", In Proc.\ IEEE Conf.\ Decision and Control, Phoenix, Dec.\ 1999, IEEE Publications, 1999, pp. 2070–2075, 1999.
- ▪E.D. Sontag, Y. Wang, "Output-to-state stability and detectability of nonlinear systems", Systems Control Lett., vol. 29, no. 5, pp. 279–290, 1997. doipdf
Abstract
The notion of input-to-state stability (ISS) has proved to be useful in nonlinear systems analysis. This paper discusses a dual notion, output-to-state stability (OSS). A characterization is provided in terms of a dissipation inequality involving storage (Lyapunov) functions. Combining ISS and OSS there results the notion of input/output-to-state stability (IOSS), which is also studied and related to the notion of detectability, the existence of observers, and output injection.
- ▪E.D. Sontag, Y. Wang, "Detectability of nonlinear systems", In Proc.\ Conf.\ on Information Sciences and Systems (CISS 96)\/, Princeton, NJ, pp. 1031–1036, 1996. pdf
Abstract
Contains a proof of a technical step, which was omitted from the journal paper due to space constraints