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On the convexity of H Riccati solutions and its applications

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2 Author(s)
Li, X.P. ; Dept. of Mech. Eng. & Mech., Drexel Univ., Philadelphia, PA, USA ; Chang, B.C.

The authors consider the two-Riccati-equation solution to a standard H control problem, which can be used to characterize all possible stabilizing optimal or suboptimal H controllers if the optimal H norm (or γ), an upper bound of a suboptimal H norm is given. Some eigen properties of these H 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 γ on the domain of interest. Based on these properties, a quadratically convergent algorithm is developed to compute the optimal H norm

Published in:

Automatic Control, IEEE Transactions on  (Volume:38 ,  Issue: 6 )