>> a1=tf({[1],[2];[3],[4]},{[1 3],[1 4];[2 3],[1 1]}); a2=minreal(a1*a1); a3=minreal(a1*a2); a4=minreal(a1*a3); a5=minreal(a1*a4); >> a2 a2 = From input 1 to output... 4 s^2 + 23.5 s + 33 1: ------------------------------------- s^4 + 11.5 s^3 + 48 s^2 + 85.5 s + 54 7.5 s + 19.5 2: ------------------------- s^3 + 5.5 s^2 + 9 s + 4.5 From input 2 to output... 10 s + 26 1: ----------------------- s^3 + 8 s^2 + 19 s + 12 19 s^2 + 94 s + 99 2: ----------------------------------- s^4 + 7.5 s^3 + 18 s^2 + 17.5 s + 6 Continuous-time transfer function. >> a3 a3 = From input 1 to output... 19 s^3 + 156.5 s^2 + 425.5 s + 384 1: ----------------------------------------------------------- s^6 + 15.5 s^5 + 97 s^4 + 312 s^3 + 540 s^2 + 472.5 s + 162 36 s^4 + 380.3 s^3 + 1464 s^2 + 2429 s + 1454 2: ----------------------------------------------------------------------- s^7 + 15 s^6 + 92.25 s^5 + 301 s^4 + 562.5 s^3 + 603 s^2 + 344.3 s + 81 From input 2 to output... 48 s^4 + 507 s^3 + 1952 s^2 + 3239 s + 1938 1: ---------------------------------------------------------------------- s^7 + 17.5 s^6 + 126 s^5 + 481 s^4 + 1045 s^3 + 1286 s^2 + 828 s + 216 91 s^3 + 673 s^2 + 1617 s + 1227 2: --------------------------------------------------------- s^6 + 11.5 s^5 + 51 s^4 + 112 s^3 + 130 s^2 + 76.5 s + 18 Continuous-time transfer function. >> a4 a4 = From input 1 to output... 91 s^10 + 2519 s^9 + 3.11e04 s^8 + 2.255e05 s^7 + 1.063e06 s^6 + 3.401e06 s^5 + 7.48e06 s^4 + 1.116e07 s^3 + 1.08e07 s^2 + 6.113e06 s + 1.537e06 1: ----------------------------------------------------------------------------------- s^14 + 36.5 s^13 + 610.7 s^12 + 6205 s^11 + 4.274e04 s^10 + 2.109e05 s^9 + 7.682e05 s^8 + 2.097e06 s^7 + 4.305e06 s^6 + 6.612e06 s^5 + 7.468e06 s^4 + 6.012e06 s^3 + 3.258e06 s^2 + 1.063e06 s + 1.575e05 172.5 s^11 + 4660 s^10 + 5.648e04 s^9 + 4.052e05 s^8 + 1.911e06 s^7 + 6.213e06 s^6 + 1.42e07 s^5 + 2.28e07 s^4 + 2.517e07 s^3 + 1.818e07 s^2 + 7.72e06 s + 1.459e06 2: ----------------------------------------------------------------------------------- s^15 + 33 s^14 + 499.5 s^13 + 4598 s^12 + 2.877e04 s^11 + 1.296e05 s^10 + 4.34e05 s^9 + 1.1e06 s^8 + 2.126e06 s^7 + 3.137e06 s^6 + 3.501e06 s^5 + 2.905e06 s^4 + 1.735e06 s^3 + 7.044e05 s^2 + 1.739e05 s + 1.968e04 From input 2 to output... 230 s^9 + 5868 s^8 + 6.581e04 s^7 + 4.257e05 s^6 + 1.749e06 s^5 + 4.729e06 s^4 + 8.408e06 s^3 + 9.47e06 s^2 + 6.123e06 s + 1.73e06 1: ------------------------------------------------------------------------------------- s^13 + 34 s^12 + 524.3 s^11 + 4848 s^10 + 2.995e04 s^9 + 1.304e05 s^8 + 4.109e05 s^7 + 9.477e05 s^6 + 1.597e06 s^5 + 1.94e06 s^4 + 1.65e06 s^3 + 9.299e05 s^2 + 3.11e05 s + 4.666e04 436 s^10 + 9524 s^9 + 9.187e04 s^8 + 5.148e05 s^7 + 1.854e06 s^6 + 4.477e06 s^5 + 7.337e06 s^4 + 8.052e06 s^3 + 5.66e06 s^2 + 2.301e06 s + 4.106e05 2: ----------------------------------------------------------------------------------- s^14 + 27.5 s^13 + 342.3 s^12 + 2555 s^11 + 1.278e04 s^10 + 4.532e04 s^9 + 1.176e05 s^8 + 2.271e05 s^7 + 3.281e05 s^6 + 3.534e05 s^5 + 2.796e05 s^4 + 1.578e05 s^3 + 6.011e04 s^2 + 1.385e04 s + 1458 Continuous-time transfer function. >> a5 a5 = From input 1 to output... 436 s^26 + 2.883e04 s^25 + 9.113e05 s^24 + 1.832e07 s^23 + 2.632e08 s^22 + 2.875e09 s^21 + 2.482e10 s^20 + 1.738e11 s^19 + 1.005e12 s^18 + 4.857e12 s^17 + 1.982e13 s^16 + 6.871e13 s^15 + 2.032e14 s^14 + 5.137e14 s^13 + 1.111e15 s^12 + 2.055e15 s^11 + 3.238e15 s^10 + 4.331e15 s^9 + 4.881e15 s^8 + 4.593e15 s^7 + 3.561e15 s^6 + 2.233e15 s^5 + 1.104e15 s^4 + 4.135e14 s^3 + 1.103e14 s^2 + 1.864e13 s + 1.5e12 1: --------------------------------------------------------------------------------------- s^31 + 76.5 s^30 + 2813 s^29 + 6.623e04 s^28 + 1.121e06 s^27 + 1.454e07 s^26 + 1.503e08 s^25 + 1.271e09 s^24 + 8.96e09 s^23 + 5.341e10 s^22 + 2.719e11 s^21 + 1.192e12 s^20 + 4.526e12 s^19 + 1.495e13 s^18 + 4.306e13 s^17 + 1.084e14 s^16 + 2.389e14 s^15 + 4.604e14 s^14 + 7.752e14 s^13 + 1.138e15 s^12 + 1.452e15 s^11 + 1.602e15 s^10 + 1.52e15 s^9 + 1.231e15 s^8 + 8.405e14 s^7 + 4.777e14 s^6 + 2.217e14 s^5 + 8.177e13 s^4 + 2.305e13 s^3 + 4.659e12 s^2 + 6.013e11 s + 3.719e10 826.5 s^26 + 5.328e04 s^25 + 1.641e06 s^24 + 3.216e07 s^23 + 4.5e08 s^22 + 4.788e09 s^21 + 4.025e10 s^20 + 2.744e11 s^19 + 1.544e12 s^18 + 7.269e12 s^17 + 2.887e13 s^16 + 9.739e13 s^15 + 2.802e14 s^14 + 6.895e14 s^13 + 1.451e15 s^12 + 2.611e15 s^11 + 4.004e15 s^10 + 5.21e15 s^9 + 5.715e15 s^8 + 5.234e15 s^7 + 3.949e15 s^6 + 2.411e15 s^5 + 1.161e15 s^4 + 4.237e14 s^3 + 1.101e14 s^2 + 1.815e13 s + 1.424e12 2: ------------------------------------------------------------------------------------- s^31 + 72 s^30 + 2490 s^29 + 5.508e04 s^28 + 8.756e05 s^27 + 1.066e07 s^26 + 1.032e08 s^25 + 8.179e08 s^24 + 5.399e09 s^23 + 3.011e10 s^22 + 1.433e11 s^21 + 5.873e11 s^20 + 2.083e12 s^19 + 6.422e12 s^18 + 1.727e13 s^17 + 4.057e13 s^16 + 8.337e13 s^15 + 1.498e14 s^14 + 2.352e14 s^13 + 3.22e14 s^12 + 3.83e14 s^11 + 3.942e14 s^10 + 3.488e14 s^9 + 2.634e14 s^8 + 1.679e14 s^7 + 8.908e13 s^6 + 3.861e13 s^5 + 1.331e13 s^4 + 3.508e12 s^3 + 6.636e11 s^2 + 8.02e10 s + 4.649e09 From input 2 to output... 1102 s^24 + 6.443e04 s^23 + 1.789e06 s^22 + 3.141e07 s^21 + 3.912e08 s^20 + 3.678e09 s^19 + 2.712e10 s^18 + 1.608e11 s^17 + 7.798e11 s^16 + 3.132e12 s^15 + 1.051e13 s^14 + 2.958e13 s^13 + 7.012e13 s^12 + 1.401e14 s^11 + 2.354e14 s^10 + 3.32e14 s^9 + 3.903e14 s^8 + 3.794e14 s^7 + 3.012e14 s^6 + 1.918e14 s^5 + 9.549e13 s^4 + 3.578e13 s^3 + 9.483e12 s^2 + 1.583e12 s + 1.25e11 1: ------------------------------------------------------------------------------------ s^29 + 68.5 s^28 + 2244 s^27 + 4.68e04 s^26 + 6.981e05 s^25 + 7.93e06 s^24 + 7.132e07 s^23 + 5.214e08 s^22 + 3.157e09 s^21 + 1.604e10 s^20 + 6.909e10 s^19 + 2.541e11 s^18 + 8.026e11 s^17 + 2.185e12 s^16 + 5.136e12 s^15 + 1.044e13 s^14 + 1.837e13 s^13 + 2.789e13 s^12 + 3.649e13 s^11 + 4.098e13 s^10 + 3.927e13 s^9 + 3.188e13 s^8 + 2.17e13 s^7 + 1.222e13 s^6 + 5.591e12 s^5 + 2.022e12 s^4 + 5.565e11 s^3 + 1.094e11 s^2 + 1.367e10 s + 8.163e08 2089 s^24 + 1.186e05 s^23 + 3.2e06 s^22 + 5.455e07 s^21 + 6.596e08 s^20 + 6.019e09 s^19 + 4.306e10 s^18 + 2.477e11 s^17 + 1.166e12 s^16 + 4.544e12 s^15 + 1.479e13 s^14 + 4.039e13 s^13 + 9.29e13 s^12 + 1.801e14 s^11 + 2.938e14 s^10 + 4.023e14 s^9 + 4.594e14 s^8 + 4.338e14 s^7 + 3.347e14 s^6 + 2.073e14 s^5 + 1.004e14 s^4 + 3.665e13 s^3 + 9.463e12 s^2 + 1.54e12 s + 1.187e11 2: --------------------------------------------------------------------------------------- s^29 + 64 s^28 + 1957 s^27 + 3.805e04 s^26 + 5.287e05 s^25 + 5.588e06 s^24 + 4.673e07 s^23 + 3.175e08 s^22 + 1.784e09 s^21 + 8.413e09 s^20 + 3.361e10 s^19 + 1.146e11 s^18 + 3.357e11 s^17 + 8.469e11 s^16 + 1.846e12 s^15 + 3.48e12 s^14 + 5.674e12 s^13 + 7.995e12 s^12 + 9.71e12 s^11 + 1.013e13 s^10 + 9.023e12 s^9 + 6.815e12 s^8 + 4.321e12 s^7 + 2.269e12 s^6 + 9.685e11 s^5 + 3.274e11 s^4 + 8.429e10 s^3 + 1.552e10 s^2 + 1.82e09 s + 1.02e08 Continuous-time transfer function.