leqr - H-infinity LQ gain (full state)
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:
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|