Environmental Engineering Reference
In-Depth Information
The state transition matrix of
can also be obtained from that of
N
without nu-
merical integration.
The zero-state response is input-dependent. It is the solution of the circuit at
when the input is applied at and the initial condition is
zero. Using numerical Laplace inversion with {
N
,
M
}
=
{8
,
10} [120, 121], it can be
shown that
is computed from
where
Because
we obtain
Consequently
where is a constant vector specifying the nodes to which the input of is con-
nected. It is obtained from where is a constant vector specifying the
output location of
N
. The above analysis shows that the zero-state response of
can be obtained efficiently from that of
N
without numerical integration.
In summary, the adjoint network of
N
can be solved with little extra computa-
tion given that the solution of
N
is available. The intrinsic relationship between
N
and
is summarized in Table 11.A.1
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