# disc2cont¶

Transform a discrete time system to a continuous time system using a bilinear (Tustin) transformation.

Given a discrete time system with time step $$\Delta T$$, the equivalent continuous time system is given by:

$\begin{split}\bar{A} &= \omega_0(A-I)(I + A)^{-1} \\ \bar{B} &= \sqrt{2\omega_0}(I+A)^{-1}B \\ \bar{C} &= \sqrt{2\omega_0}C(I+A)^{-1} \\ \bar{D} &= D - C(I+A)^{-1}B\end{split}$

where $$\omega_0 = \frac{2}{\Delta T}$$.

References

MIT OCW 6.245

param sys

SHARPy discrete-time state-space object.

type sys

libss.ss

returns

Converted continuous-time state-space object.

rtype

libss.ss