Persistent dwell-time switched nonlinear systems: Variation paradigm and gauge design

Abstract

Asymptotic gain and adaptive control are studied for persistent dwell-time switched systems. Ultimate variations of auxiliary functions are considered for existence of asymptotic gain and a gauge design is introduced for switching-uniform adaptive control by partial state feedback and output feedback of switched systems subject to unmeasured dynamics and persistent dwell-time switching. The usage of the controlled dynamics as a gauge for the instability mode of the unmeasured dynamics makes it possible to design a control rendering the evolution of the overall system interchangeably driven by the stable modes of the controlled and unmeasured dynamics. Unmeasured-state dependent control gains are dealt with and unknown time-varying parameters are attenuated via asymptotic gain. Verification of asymptotic gain conditions is based on the relation between dissipation rates of unmeasured dynamics and timing characterizations Tp and Tp of switching sequences. © 2010 IEEE.