Time-Delay system simulation.zip

% The simulation of time-delay systems % Copyright (C2012-2015) Yang XIAO, Beijing Jiaotong University, Aug.10, 2012, E-Mail: yxiao@bjtu.edu.cn. % In our book [1], we 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 % 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. % clear; % delay parameters t1=.4; t2=.5; t3=.169; t4=0.26; % Solve the time-delay system equation % dx(t)/dt=Ax(t)+B1x(t-t1)+B2x(t-t2)+B3x(t-t1)+B4x(t-t4) sol = dde23('yxiao_fun1',[t1,t2,t3,t4],ones(4,1),[0, 50]); % plot the system states plot(sol.x,sol.y); title('System States') xlabel('Time/s'); ylabel('x1(t),x2(t),x3(t),x4(t)');