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370 STATE SPACE ANALYSIS [CHAP. 7
where
As in the discrete-time case, Eqs. (7.19~) and (7.19b) are called an N-dimensional state
space representation (or state equations) of the system, and the N x N matrix A is termed
the system matrix. In general, state equations of a single-input single-output continuous-
time LTI system are given by
As in the discrete-time case, there are infinitely many choices of state variables for any
given system. The solution of Eqs. (7.20a) and (7.206) for a given initial state are discussed
in Sec. 7.6.
B. Multiple-Input Multiple-Output Systems:
If a continuous-time LTI system has m inputs, p outputs, and N state variables, then a
state space representation of the system can be expressed as
q(t) = Aq(t) + Bx(t)
YO) = Cq(t) + Dx(t)
where
and
NxN :I
A=
lpxN
