disc2contΒΆ
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