- ▪E.D. Sontag, "Input-to-State Stability", In Encyclopedia of Systems and Control, pp. 1-9, 2020. pdfinput to state stability · integral input to state stability · iISS · ISS · input to output stability
Abstract
The notion of input to state stability (ISS) qualitatively describes stability of the mapping from initial states and inputs to internal states (and more generally outputs). This encyclopedia-style article entry gives a brief introduction to the definition of ISS and a discussion of equivalent characterizations. It is an update of the article in the 2015 edition, including additional citations to recent PDE work.
- ▪E.D. Sontag, "Input-to-State Stability", In Encyclopedia of Systems and Control, 2015. pdfinput to state stability · integral input to state stability · iISS · ISS · input to output stability
Abstract
The notion of input to state stability (ISS) qualitatively describes stability of the mapping from initial states and inputs to internal states (and more generally outputs). This entry focuses on the definition of ISS and a discussion of equivalent characterizations.
- ▪E.D. Sontag, "Input to State Stability", In The Control Systems Handbook: Control System Advanced Methods, Second Edition., pp. 45.1-45.21 (1034-1054), 2011. pdfinput to state stability · integral input to state stability · iISS · ISS · input to output stability
Abstract
An encyclopedia-type article on foundations of ISS.
- ▪D. Angeli, B.P. Ingalls, E.D. Sontag, Y. Wang, "Separation principles for input-output and integral-input-to-state stability", SIAM J. Control Optim., vol. 43, no. 1, pp. 256–276, 2004. doipdfinput to state stability · integral input to state stability · iISS · ISS · input to output stability
Abstract
We present new characterizations of input-output-to-state stability. This is a notion of detectability formulated in the ISS framework. Equivalent properties are presented in terms of asymptotic estimates of the state trajectories based on the magnitudes of the external input and output signals. These results provide a set of "separation principles" for input-output-to-state stability , characterizations of the property in terms of weaker stability notions. When applied to the closely related notion of integral ISS, these characterizations yield analogous results.
- ▪E.D. Sontag, "The ISS philosophy as a unifying framework for stability-like behavior", In Nonlinear control in the year 2000, Vol.\ 2 (Paris), pp. 443–467, 2001. pdfinput to state stability · integral input to state stability · iISS · ISS · input to output stability
Abstract
(This is an expository paper prepared for a plenary talk given at the Second Nonlinear Control Network Workshop, Paris, June 9, 2000.) The input to state stability (ISS) paradigm is motivated as a generalization of classical linear systems concepts under coordinate changes. A summary is provided of the main theoretical results concerning ISS and related notions of input/output stability and detectability. A bibliography is also included, listing extensions, applications, and other current work.
- ▪B.P. Ingalls, E.D. Sontag, Y. Wang, "Remarks on input to output stability", In Proc.\ IEEE Conf.\ Decision and Control, Phoenix, Dec.\ 1999, IEEE Publications, 1999, pp. 1226–1231, 1999.
- ▪E.D. Sontag, Y. Wang, "Notions of input to output stability", Systems Control Lett., vol. 38, no. 4-5, pp. 235–248, 1999. pdf
Abstract
This paper deals with several related notions of output stability with respect to inputs (which may be thought of as disturbances). The main such notion is called input to output stability (IOS), and it reduces to input to state stability (ISS) when the output equals the complete state. For systems with no inputs, IOS provides a generalization of the classical concept of partial stability. Several variants, which formalize in different manners the transient behavior, are introduced. The main results provide a comparison among these notions