On the convexity of H/sup infinity / Riccati solutions and its applications

The authors consider the two-Riccati-equation solution to a standard H/sup infinity / control problem, which can be used to characterize all possible stabilizing optimal or suboptimal H/sup infinity / controllers if the optimal H/sup infinity / norm (or gamma ), an upper bound of a suboptimal H/sup infinity / norm is given. Some eigen properties of these H/sup infinity / Riccati solutions are revealed. The most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma on the domain of interest. Based on these properties, a quadratically convergent algorithm is developed to compute the optimal H/sup infinity / norm.<
>