Input-to-State Stability and Averaging of Linear Fast Switching Systems
Wei Wang, Dragan Nesic
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC | Published : 2010
We consider the averaging method for stability of rapidly switching linear systems with disturbances. We show that the notions of strong and weak averages proposed in , with partial strong average defined in this note, play an important role in the context of switched systems. Using these notions of average, we show that exponential input-to-state stability (ISS) of the strong and the partial strong average system with linear gain imply exponential ISS with linear gain of the actual system. Similarly, exponential ISS of the weak average guarantees an appropriate exponential derivative ISS (DISS) property for the actual system. Moreover, using the Lyapunov method, we show that linear ISS g..View full abstract
Manuscript received October 11, 2009; revised October 14, 2009 and November 29, 2009. First published February 08, 2010; current version published May 12, 2010. This work was supported by the Future Fellow and Discovery Grants Scheme. Recommended by Associate Editor J. H. Braslavsky.