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LME Reference — linear algebra 331 With two or three output arguments, (X,L,K) = care(...) also returns the gain matrix K defined as K = R−1 B0 X and the column vector of closed-loop eigenvalues L = eig(A − BK) care(A,S,Q,true) with up to two output arguments is equivalent to care(A,B,Q) or care(A,B,Q,false) with S=B*B’. Example A = B = C = Q = R = (X, X [-4,2;1,2]; [0;1]; [2,-1]; C’ * C; 5; L, K) = care(A, B, Q, R) = 1.07 3.5169 3.5169 23.2415 L = -4.3488 -2.2995 K = 0.7034 4.6483 A’ * X + X * A - X * B / R * B’ * X + Q 1.7319e-14 1.1369e-13 8.5265e-14 6.2528e-13 See also dare chol Cholesky decomposition. Syntax M2 = chol(M1) Description If a square matrix M1 is symmetric (or hermitian) and positive definite, it can be decomposed into the following product: M1 = M02 M2
