dare validation unsuitable for H-inf synthesis #440
Description
The command dare(A, B, Q, R) has validation on R > 0, this is unsuitable for H-infinity synthesis.
finding the stationary H-inf controller amounts to finding a fixpoint to the dare:
P = Q + A'(P^(-1) + BR^(-1)B -I/gamma^2)A.
This is equivalent to solving the lqr problem with augmented B* = [B I] and R* = [R 0;0 -gamma^2]. The algorithm which is already implemented works well, however R* is indefinite so calling dare(A, B, Q, R) throws an error.
Minimal test case:
gamma = 2
A = ones((1,1))
B = ones((1,2))
Q = ones((1,1))
R = [1. 0;0 -gamma^2]
P = dare(A,B,Q,R)
@test P[1,1] \approx 1/2 + sqrt(4/3 + 1/4)