The Eqs. (12.2) and (12.3) describe an
th-order linear time-invariant single-input-single-output
system. For linear multi-input-multi-output systems of order
with 
inputs
and 
outputs
these equations become
| state vector |
 |
(
 ) vector |
| input vector |
 |
(
 ) vector |
| output vector |
 |
(
 ) vector |
| system matrix |
 |
(
 ) matrix |
| input matrix |
 |
(
 ) matrix |
| output matrix |
 |
(
 )
matrix |
| feedthrough matrix |
 |
(
 ) matrix |
It goes without saying that the general representation of
Eqs. (12.4) and (12.5) also includes the
single-input-single-output case. The matrices
and
have constants elements. If these elements
are time-varying, the matrices of the corresponding
time-varying system are substituted by
matrix functions of time, e.g.
.
with the 
