Efficient computation of the infimum in H∞ control for seismic structures
An important consideration in the design of H∞ controllers is the optimal norm of the H∞ control problem. This value determines the lowest value of the H∞ norm that can be obtained with the problem and system defined. Hence, it represents a design limit, but one that is computationally intractable and difficult to obtain. A new method for determining the optimal H∞ norm of a state feedback system is presented. It is based on the application of discriminant to check a stability condition on the Hamiltonian matrix that is associated with the infimum value. In addition, a generalized eigenvalue problem is deduced from the discriminant stability condition to avoid any required iteration. The overall approach provides a highly accurate approximation of the optimal value with minimum computation compared to other approaches in the literature.