ABSTRACT
The state-space approach to H∞ optimization problem proposed by DGKF [1] is a powerful tool for robust controller design. It can be used to characterize all possible stabilizing optimal (suboptimal) controllers. However, in order to develop an efficient algorithm, the properties of indefinite Riccati equations should be investigated. In this paper, some properties of these H∞ Riccati solutions are revealed. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of γ in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H∞ norm.
