A recursive construction algorithm for covariance control
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This paper proposes an algorithm to compute solutions X to the linear matrix equation and inequality of the type (I - BB+)(AX + XA + W)(I - BB+) = 0, X > 0. This problem arises in the synthesis of covariance controllers; the set of symmetric matrices X assignable as a dosed-loop state covariance by a stabilizing controller is characterized by these conditions. Our algorithm generates analytical solutions to the above problem in a recursive manner. In this sense, our algorithm is essentially different from other computational methods pertinent to this problem, such as convex programming. As a result, the algorithm does not involve the issue of convergence and terminates in an a priori known finite number of steps. Thus, the computational complexity is expected to be much less than that of other methods.
IEEE Transactions on Automatic Control
author list (cited authors)
Iwasaki, T., Skelton, R. E., & Corless, M.
complete list of authors
Iwasaki, T||Skelton, RE||Corless, M