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

Table 1

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

Time/s	𝑡=0.2	𝑡=0.4	𝑡=0.6	𝑡=0.8	𝑡=1.0	𝑡=10
Analytical solution	1−𝑒^−0.42	1−𝑒^−0.82	1−𝑒^−1.22	1−𝑒^−1.62	1−𝑒^−2.02	1−𝑒^−202
Numerical solution	0.1648399769821804	0.2753355179413893	0.3494028940438990	0.3990517410026724	0.4323323583816937	0.4999999989694231
Absolute error (×10^−17)	4.211244565981330	6.964767980438173	6.327555838522091	8.193205378981371	0.5211907116443345	9.037574721516070