System Identification Toolbox

Continuous-Time State-Space Models

It is often easier to describe a system from physical modeling in terms of a continuous-time model. The reason is that most physical laws are expressed in continuous time as differential equations. Therefore, physical modeling typically leads to state-space descriptions like

(3-26)

Here, means the time derivative of . If the input is piece-wise constant over time intervals , then the relationship between and can be exactly expressed by (3-21) by taking

(3-27)

and associate with , etc. If you start with a continuous-time innovations form

(3-28)

the discrete-time counterpart is given by (3-23) where still the relationships (3-27) hold. The exact connection between and is somewhat more complicated, though. An ad hoc solution is to use

(3-29)

in analogy with G and B. This is a good approximation for short sampling intervals T.

State-Space Representation of Transfer Functions

Estimating Impulse Responses