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Problem 7.15PP
Given the system
* = [ _ 2
with zero initial conditions, find the steady-state value of x for a step input u.
Step-by-step solution
step 1 of 1
Write the general form of state space equation.
Write the general form of state space equation.
± = A x + B u ...... (1)
Consider the value of t a t steady state condition with zero initial condition.
i = 0 ..... (2)
Consider the value of wat unit step input condition. 
a = I ...... (3)
Consider the value of xat steady state condition.
x = ...... (4)
Consider the value of matrix a •
"=L-2 -.J
Consider the value of matrix b •
...... (6)
Substitute equations (2), (3) and (4) in equation (1). 
0 = A x ,+ B 
-B = A x ,
-B
A
-B A -‘ - X . ...... (7)
Substitute equations (5) and (6) in equation (7).
- m - j '
Hence, the steady state value of x is