Continuous-Time System Models

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:

  • State-space form

  • Partial fraction expansion

  • Transfer function

  • Zero-pole-gain form

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, A, B, C, and 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, residue determines the partial fraction expansion of the system. See the description of 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.