Input-to-State Stability of Time-Delay Systems: A Link With Exponential Stability

Nima Yeganefar, Pierdomenico Pepe, Michel Dambrine
2008 IEEE Transactions on Automatic Control  
The main contribution of this technical note is to establish a link between the exponential stability of an unforced system and the input-to-state stability (ISS) via the Liapunov-Krasovskii methodology. It is proved that a system which is (globally, locally) exponentially stable in the unforced case is (globally, locally) input-to-state stable when it is forced by a measurable and locally essentially bounded input, provided that the functional describing the dynamics in the unforced case is
more » ... obally, on bounded sets) Lipschitz and the functional describing the dynamics in the forced case satisfies a Lipschitz-like hypothesis with respect to the input. Moreover, a new feedback control law is provided for delay-free linearizable and stabilizable time-delay systems, whose dynamics is described by locally Lipschitz functionals, by which the closed-loop system is ISS with respect to disturbances adding to the control law, a typical problem due to actuator errors. Index Terms-Exponential stability, input-to-state stability (ISS), Liapunov-Krasovskii theorem, nonlinear time-delay systems.
doi:10.1109/tac.2008.928340 fatcat:guikyjeccvabfmaewtxwconz2m