Description |
In our book [1], we proposed some stability test theorems for linear time-delay system.
To verify our stability test theorems and others' stability test algorithms [2], we provide this simulation program of time-delay systems.
You can use the program, to find that the results of [2] are incorrecct.
The following example is taken from the case 1 of [2], where [2] claimed to found a stable region for the time-delay system of case 1,however, the simulation shows that the time-delay system of case 1 is unstable,
dx(t)/dt=Ax(t)+B1x(t-t1)+B2x(t-t2)+B3x(t-t1)+B4x(t-t4)
with delay parameters: t1=.4;t2=.5; t3=.169;t4=0.26.
Thus, the main results of [2] are incorrect.
[1] Yang Xiao, Yingkang Zhang, Multidimensional Signal Processing and
Multidimensional Systems, Publishing House of Electronics Industry,
Beijing, 2011.
[2] Rifat Sipahi and Ismail Ilker Delice, Advanced Clustering With Frequency Sweeping Methodology for the Stability Analysis of Multiple Time-Delay Systems,IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 56, NO. 2, 2011, pp.467-472. |