Further equivalences and semiglobal versions of integral input to state stability

Details Further equivalences and semiglobal versions of integral input to state stability Further equivalences and semiglobal versions of integral input to state stability

1999-08-13

arxiv.org/abs/math/9908066v1

Mathematics

Optimization and Control

See web site http://www.math.rutgers.edu/~sontag for related work

Scientific paper

This paper continues the study of the integral input-to-state stability (IISS) property. It is shown that the IISS property is equivalent to one which arises from the consideration of mixed norms on states and inputs, as well as to the superposition of a ``bounded energy bounded state'' requirement and the global asymptotic stability of the unforced system. A semiglobal version of IISS is shown to imply the global version, though a counterexample shows that the analogous fact fails for input to state stability (ISS). The results in this note complete the basic theoretical picture regarding IISS and ISS.

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