A RECURSIVE CONSTRUCTION ALGORITHM FOR COVARIANCE CONTROL

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 c ontrollers; the set of symmetric matrices X assignable as a closed-loo p state covariance by a stabilizing controller is characterized by the se conditions. Our algorithm generates analytical solutions to the abo ve problem in a recursive manner. In this sense, our algorithm is esse ntially different from other computational methods pertinent to this p roblem, such as convex programming. As a result, the algorithm does no t involve the issue of convergence and terminates in an a priori known finite number of steps. Thus, the computational complexity is expecte d to be much less than that of other methods.