Computation of Gram Matrix and Its Partial Derivative Using Precise Integration Method for Linear Time-Invariant Systems

Table 2

Analytical solution and numerical solution using precise integration method of 𝐖^𝑡_𝐶1.

Time/s	𝑡=0.2	𝑡=0.4	𝑡=0.6	𝑡=0.8	𝑡=1.0
Analytical solution	14−720𝑒^0.4	14−920𝑒^0.8	14−1120𝑒^1.2	14−1320𝑒^1.6	14−1520𝑒^2
Numerical solution	0.01538798388752625	0.04780196614725030	0.08434318344828887	0.1187672633034740	0.1484985375725405
Absolute error (×10^−17)	0.6580362078975456	1.966176961971875	1.964307811561096	2.324494307987107	1.99377149409639