Input to State Stability and Related Notions

The analysis of input/output stability is one of the fundamental issues in control theory. External inputs might represent disturbances, estimation errors, or tracking signals, and outputs may correspond to the entire state, or to a more general quantity such as a tracking or regulation error, or the distance to a target set of states such as a desired periodic orbit. For linear systems, one characterizes i/o stability through finiteness of gains (operator norms). A nonlinear generalization is provided by input to state stability (ISS). This paper summarizes some of the main theoretical results concerning ISS and related notions such as integral ISS (energy bounds), output to input stability (a notion of “minimum-phase” system), and input/output to state stability (a notion of detectability). It also describes, as an illustrative application, an observer design methodology for certain kinetic networks which is based on ISS ideas.