Synchronization of Bidirectionally Coupled Nonlinear Systems with Time-Varying Delay

This chapter considers the synchronization problem for coupled nonlinear systems with time-varying delay. In previous work, we have derived a sufficient condition for synchronization and boundedness of two identical strictly semi-passive systems coupled using state feedback with time-delay. This condition, however, requires that all state components are mutually coupled and the coupling delay is constant. In this chapter we extend the conditions to identical systems coupled using output feedback with time-varying delay where a bound on the length of the delay and an upper bound of its time-derivative are known. Firstly, we show. using the small-gain theorem, that the trajectories of coupled strictly semi-dissipative systems converge to a bounded region. Then we derive a sufficient condition for synchronization of the systems coupled with time-varying delay by using a delay range dependent stability criterion.