[VCLab Main] [Back to Bode Plot] [LTI System]

The basic representation for linear systems is the
*linear state equation*, customarily written
in the standard form

(1) |

where the overdot denotes differentiation with respect
to time *t*. The
vector function of time
*x*(*t*) is called the *state
vector*, and its components,
, are the *state
variables*. The *input signal* is the
function *u*(*t*),
and *y*(*t*) is the
*output
signal*. We assume throughout that
.

Default assumptions on the coefficient matrices in (1)
are that the entries of
, and
are continuous, real-valued functions defined for all
. Standard terminology is that (1) is *linear
time invariant* (**LTI**) if these coefficient matrices are
constant. The linear state equation is called *time
varying* if any coefficient matrix varies with time.

[VCLab Main] [Back to Bode Plot] [LTI System]

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