Lyapunov stability analysis for nonlinear systems with state-dependent state delay

Abstract

This paper addresses the stability problem for systems with state-dependent state delay (delay which involves the state of the system). Different from the time-dependent delay, the state dependence of the delay makes the value of delay dependent on the state change, which indicates that it is impossible to exactly know a priori how far in the history the state-information is needed. We apply the Lyapunov stability theory to obtain sufficient conditions for exponential stability of the zero equilibrium. Then we apply those results to some specific examples to illustrate the effectiveness of the approach and our general results. A class of stabilizing memoryless controllers for a second-order system with state-dependent state delay is also proposed.