Lower Bound for Discrete-Time H∞ Control Performance

The paper aims to provide an approach to obtain a lower bound of H-infinity control performance in state space. It is not involved Riccati equation and only concerns with the solution to the standard H-2 Riccati equation. As a consequence, the approach can help one to narrow the optimal H-infinity 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-infinity performance including the optimal control and H-infinity control performance, the optimal estimation and the H-infinity estimation, but also the impact of the multiple-channel disturbances or previewable disturbance on the H-infinity control performance.