framework of localized sets [@pereira07]. The concept of localized sets opens up the possibility of an easy and an efficient way to detect CPS especially in complicated non-phase-coherent attractors of time-delay systems. The main ingredient of this technique is to define an event in one of the systems and then observe the other during the event, which defines a set $D$. Depending upon the property of this set $D$, one can state whether PS exists or not. The set is spread over the entire attractor for asynchronous systems, whereas it is localized on the attractor if the coupled systems are mutually phase-locked or in phase synchronous state.

We use the above three different frameworks to confirm the existence of GPS in an array of piecewise linear time-delay systems in the following.

\[sec:level2\]GPS in a Linear Array of Time-delay Systems with piecewise linearity
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Recently, we have reported the dynamical organization of an array of Mackey-Glass time-delay systems in chaotic regime to form global phase synchronization (GPS) via sequential synchronization [@suresh10], as mentioned in the introduction. In this section, we intend to examine the generic nature of the results in Ref. [@suresh10], by investigating the emergence of GPS in an array 