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Please note that the recommended version of Scilab is 2025.0.0. This page might be outdated.
See the recommended documentation of this function
leqr
H-infinity LQ gain (full state)
Calling Sequence
[K,X,err]=leqr(P12,Vx)
Arguments
- P12
syslin
list- Vx
symmetric nonnegative matrix (should be small enough)
- K,X
two real matrices
- err
a real number (l1 norm of LHS of Riccati equation)
Description
leqr
computes the linear suboptimal H-infinity LQ full-state gain
for the plant P12=[A,B2,C1,D12]
in continuous or discrete time.
P12
is a syslin
list (e.g. P12=syslin('c',A,B2,C1,D12)
).
[C1' ] [Q S] [ ] * [C1 D12] = [ ] [D12'] [S' R]
Vx
is related to the variance matrix of the noise w
perturbing x
;
(usually Vx=gama^-2*B1*B1'
).
The gain K
is such that A + B2*K
is stable.
X
is the stabilizing solution of the Riccati equation.
For a continuous plant:
K=-inv(R)*(B2'*X+S)
For a discrete time plant:
with Abar=A-B2*inv(R)*S'
and Qbar=Q-S*inv(R)*S'
The 3-blocks matrix pencils associated with these Riccati equations are:
discrete continuous |I -Vx 0| | A 0 B2| |I 0 0| | A Vx B2| z|0 A' 0| - |-Q I -S| s|0 I 0| - |-Q -A' -S | |0 B2' 0| | S' 0 R| |0 0 0| | S' -B2' R|
See Also
- lqr — LQ compensator (full state)
Authors
F.D.;
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