Specifications

dlqr
16-60
16dlqr
Purpose Design linear-quadratic (LQ) state-feedback regulator for discrete-time plant
Syntax [K,S,e] = dlqr(a,b,Q,R)
[K,S,e] = dlqr(a,b,Q,R,N)
Description [K,S,e] = dlqr(a,b,Q,R,N) calculates the optimal gain matrix K such that
the state-feedback law
minimizes the quadratic cost function
for the discrete-time state-space mode
l
The default value
N=0 is assumed when N is omitted.
In addition to the state-feedback gain
K, dlqr returns the infinite horizon
solution S of the associated discrete-time Riccati equation
and the closed-loop eigenvalues
e = eig(a-b*K).NotethatK is derived from
S by
Limitations The problem data must satisfy:
• The pair is stabilizable.
• and .
• has no unobservable mode on the unit circle.
See Also dare Solve discrete Riccati equations
lqgreg LQG regulator
un
[]
Kx n
[]
–=
Ju
()
xn
[]
T
Qx n
[]
un
[]
T
Ru n
[]
2xn
[]
T
Nu n
[]
++
()
n 1=
∞
å
=
xn 1+
[]
Ax n
[]
Bu n
[]
+=
A
T
SA S– A
T
SB N+
()
B
T
SB R+
()
1–
B
T
SA N
T
+
()
– Q+ 0=
KB
T
SB R+
()
1–
B
T
SA N
T
+
()
=
AB
,()
R 0
>
QNR
1–
N
T
– 0
≥
QNR
1–
N
T
– ABR
1–
N
T
–,()