Page 395 - Schaum's Outline of Theory and Problems of Signals and Systems
P. 395
STATE SPACE ANALYSIS [CHAP. 7
Fig. 7-6
Rearranging and writing in matrix form, we get
where
STATE EQUATIONS OF DISCRETE-TIME LTI =STEMS DESCRIBED
BY DIFFERENCE EQUATIONS
7.7. Find state equations of a discrete-time system described by
y[n] - fy[n - 11 + $y[n - 21 =x[n]
Choose the state variables q,[n] and q2[n] as
41[nl =y[n - 21
4JnI =y[n - 11
Then from EqsJ7.79) and (7.80) we have
4dn + 11 =q,[nI
42[n + 11 = -$ql[n] + $?2[n] +x[n]
Y[~I -$sJnI + %2[nI +-+I
=
In matrix form
