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A special case of discrete-continuous systems (BPS) is considered: linear-quadratic in the state of BPS with controllable coefficients. For this class of systems, an analogue of the Krotov global improvement method is constructed, the last iteration of which gives a solution in the form of an approximately optimal control synthesis. The obtained result can be interpreted as the development of the theory of analytical design of optimal regulators (ACOR) with reference to CSN. An illustrative example is given.