Consider an LQ problem: \(\min_{K\in \Omega}J(K)\) subject to \(\dot x=Ax+Bu\), \(y=Cx\), where \(J(K)=0.5\int^{\infty}_{0}x'(Q+K'RK)xdt\), \(\Omega =\{K:\) \(F(K)=0\}\); \(F(K)=K(I-C'(CC')^{-1}C)\), \(F(K)=K- diag\{K_ 1,...,K_ M\}\) for output, decentralised (with M local agents) feedback control, respectively. Two theorems are proved: Suppose \(K+L=R^{-1}B'P\), where K is the gain matrix, L is an arbitrary matrix. P, \(P^*\) are the positive definite solutions of the Riccati equation for \(Q\leftarrow Q+L\), \(L=0\), respectively. Then the matrix (A-BK) is asymptotically stable and the performance index is given by \(J=0.5x(O)'Px(O)\geq 0.5x(O)'P^*x(O)=J^*\). The results are supplemented by the numerical simulation of a load-frequency control problem.