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what is root of a equation in s(laplace domain) in response of ilapalace means

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syms s t
num11 = [0.005659 0.05206 0.004496];
den11 = [1 9.357 2.228 0.06147];
a11=tf(num11,den11);
G11 = poly2sym(num11,s)/poly2sym(den11,s);
num12=[0.003013];
den12=[1 9.357 2.228 0.06147];
a12=tf(num12,den12);
G12 = poly2sym(num12, s)/poly2sym(den12, s);
num21=[0.003013];
den21=[1 9.357 2.228 0.06147];
a21=tf(num21,den21);
G21= poly2sym(num21,s)/poly2sym(den21,s);
num22=[0.005659 0.02714 0.004051];
den22=[1 9.357 2.228 0.06147];
a22=tf(num22,den22);
G22=poly2sym(num22,s)/poly2sym(den22,s)
num31=[0.0006678 0.003046];
den31=[1 9.357 2.228 0.06147];
a31=tf(num31,den31);
G31= poly2sym(num31,s)/poly2sym(den31,s)
num32=[0.02554 0.004018];
den32=[1 9.357 2.228 0.06147];
a32=tf(num32,den32);
G32= poly2sym(num32,s)/poly2sym(den32,s);
GP=[G11 G12;G21 G22;G31 G32]
ilaplace(GP,s,t)
the output came (its very long to post here just run the programm once and see the output and in that output it is in terms of s again what to make of that
any explaination

Accepted Answer

Paul
Paul on 25 Jul 2021
If ilaplace can't find a closed form expression it returns the result in terms of "root," which can then be evaluated numerically if needed. For example:
>> vpa(ilaplace(GP),5)
ans =
[ 0.0017395*exp(-0.03183*t) + 5.9665e-7*exp(-9.1133*t) + 0.0039189*exp(-0.21191*t), 0.0018424*exp(-0.03183*t) + 0.000037273*exp(-9.1133*t) - 0.0018797*exp(-0.21191*t)]
[ 0.0018424*exp(-0.03183*t) + 0.000037273*exp(-9.1133*t) - 0.0018797*exp(-0.21191*t), 0.0019524*exp(-0.03183*t) + 0.0028045*exp(-9.1133*t) + 0.00090214*exp(-0.21191*t)]
[ 0.0018496*exp(-0.03183*t) - 0.000037605*exp(-9.1133*t) - 0.001812*exp(-0.21191*t), 0.0019598*exp(-0.03183*t) - 0.0028296*exp(-9.1133*t) + 0.00086974*exp(-0.21191*t)]

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