The output feedback stabilization problem for a dynamic object with phase constraints is considered. It is shown that the solution of the problem in the case of a reduced-order controller is reduced to the search of two mutually inverse matrices satisfying matrix inequalities. A search algorithm for these matrices is proposed and its convergence conditions are shown. A model for an inverted pendulum on a cart has been constructed and its output feedback stabilization problems for full and reduced order controllers in the case of constraints on the object phase variables have been solved.
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