H∞ control state feedback and Rayleigh quotient Original Research Article

Based on the analogy between structural mechanics and optimal control, the optimal parameter γ−2cr of state feedback H∞ control is shown to correspond to the fundamental Rayleigh quotient eigenvalue in structural stability or to structural vibration problems formulated in the prismatic domain. The derivation is based on the variational method and the related Riccati differential equation. Thereafter, the precise integration method is developed for time invariant systems and leads to numerical results which achieve full computer precision. Additionally, the optimal parameter γcr−2 can be computed to any required precision by using the extended Wittrick–Williams algorithm.