Lower bound for discrete-time H∞ control performance

The paper aims to provide an approach to obtain a lower bound of H_∞ control performance in state space. It is not involved Riccati equation and only concerns 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.