The paper aims to provide an approach to obtain a lower bound of H∞ control performance in state space. It is not involved in algebraic manipulation of Riccati equation and only concerned with the solution to the standard H₂ Riccati equation. As a consequence, the approach can help one to narrow the optimal H∞ performance search via bisection method to a smaller range and considerably reduce the search cost. In addition, the approach enables us to have an insight into not only the link and difference between the optimal performance and the H∞ performance including the optimal control and H∞ control performance, the optimal estimation and the H∞ estimation, but also the impact of the multiple-channel disturbances or previewable disturbance on the H∞control performance.