Specifications

lqr
16-121
16lqr
Purpose Design linear-quadratic (LQ) state-feedback regulator for continuous plant
Syntax [K,S,e] = lqr(A,B,Q,R)
[K,S,e] = lqr(A,B,Q,R,N)
Description [K,S,e] = lqr(A,B,Q,R,N) calculates the optimalgainmatrix K suchthatthe
state-feedback law
minimizes the quadratic cost function
for the continuous-time state-space model
The default value
N=0 is assumed when N is omitted.
In addition to the state-feedback gain
K, lqr returns the solution S of the
associated Riccati equation
and the closed-loop eigenvalues
e = eig(A-B*K). Note that is derived from
by
Limitations The problem data must satisfy:
• The pair is stabilizable.
• and .
• has no unobservable mode on the imaginary
axis.
See Also care Solve continuous Riccati equations
dlqr State-feedback LQ regulator for discrete plant
lqgreg Form LQG regulator
lqrd Discrete LQ regulator for continuous plant
lqry State-feedback LQ regulator with output weighting
uKx–=
Ju
()
x
T
Qx u
T
Ru 2x
T
Nu++
()
td
0
∞
ò
=
x
·
Ax Bu+=
A
T
SSA SBN+
()
R
1–
B
T
SN
T
+
()
– Q++0=
K
S
KR
1–
B
T
SN
T
+
()
=
AB
,()
R 0
>
QNR
1–
N
T
– 0
≥
QNR
1–
N
T
– ABR
1–
N
T
–
,()