1999/08/13 by David Angeli, Eduardo D. Sontag, Eduardo Sontag +5
Engineering · Mathematics · #Adaptive Control of Nonlinear Systems #Control and Stability of Dynamical Systems #Stability and Control of Uncertain Systems #math.DS #math.OC #msc:93B36 #msc:93C15 #msc:93D20
paper · pdf · doi:10.48550/arxiv.math/9908066
See web site http://www.math.rutgers.edu/~sontag for related work
arxiv created 1999/08/13 · arxiv updated 2009/11/30
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.