SAMPLED-DATA SIMULATION OF PERIODICALLY SWITCHED LINEAR CIRCUITS - Computer Methods for Analysis of Mixed-Mode Switching Circuits - page 115

Assume a switching occurs at and the network variables of
the circuit immediately before switching is given by

To yield

from a forward step from to is

taken first, as shown graphically in Fig.6.2. The response at
is obtained from

The step size T should be chosen such that no switching at
i.e. Step size different from that of
other steps can be used in this step to ensure the continuity of at

Following the forward step, the time origin is reset to
The initial condition is subsequently given by and the input
becomes A backward step of the same step size
from to is then taken to compute
Because Laplace transform is defined from

to only, to

accommodate the backward step, the transform

is employed. In the the time origin is and

the input becomes The circuit in the during

is depicted by

Using Laplace transform in the backward step, we obtain the response
at the time instant immediately after switching

where