and $x_{N}=x_{N-1}$. The nonlinear function $f(x)$ is chosen to be a piecewise linear function defined as $$\begin{aligned}
f(x)=
\left\{
\begin{array}{cc}
0, &  x \leq -4/3  \\
            -1.5x-2,&  -4/3 < x \leq -0.8 \\
            x,&  -0.8 < x \leq 0.8 \\
            -1.5x+2,&  -0.8 < x \leq 4/3 \\
0, &  x > 4/3.
         \end{array} \right.\end{aligned}$$

![\[fig1b\] Plot of the first ten maximal Lyapunov exponents $\lambda_{max}$ of the piecewise linear time-delay system (\[eq\_1\]a) for the parameter values $\beta=1.0$, $\alpha_{1}=1.2, \tau \in(3,25)$.](piece_wise_lya){width="0.7\columnwidth"}

The system parameters are fixed as follows: $\beta = 1.0$, $\alpha_1=1.2$, $\tau = 15.0$. The values of the nonlinear parameter $\alpha_i$ of the response systems in the array are chosen randomly in the range $\alpha_{i} \in (1.19,1.23)$, so that all the subsystems are effectively nonidentical due to the parameter mismatch. The original non-phase-coherent hyperchaotic attractor of the drive in the $(x(t),x(t-\tau))$ state space is illustrated in Fig. \[fig1\](a). The corresponding transformed attractor, effected using the transformation (\[eq\_2\]), in the new state space ($x(t+\tau),z(t+\tau)$) is depicted in Fig. \[fig1\] (b), which now looks like a smeared limit cycle-like attractor with a single center of rotation. The optimal value of the $\hat{\tau}$ in (\[eq\_2\]) for the above piecewise linear time-delay systems is found 