The continuous-time system models are representational schemes for analog filters. Many of the discrete-time system models described earlier are also appropriate for the representation of continuous-time systems:
Partial fraction expansion
It is possible to represent any system of linear time-invariant differential equations as a set of first-order differential equations. In matrix or state-space form, you can express the equations as
where u is a vector of nu inputs, x is
an nx-element state vector, and y is
a vector of ny outputs. In the MATLAB® environment,
D are stored in separate rectangular arrays.
An equivalent representation of the state-space system is the Laplace transform transfer function description
For single-input, single-output systems, this form is given by
Given the coefficients of a Laplace transform transfer function,
the partial fraction expansion of the system. See the description
residue for details.
The factored zero-pole-gain form is
As in the discrete-time case, the MATLAB environment stores polynomial coefficients in row vectors in descending powers of s. It stores polynomial roots, or zeros and poles, in column vectors.