<![CDATA[The paper deals with developing backgrounds to study and design the controllers for a wide class of dynamical systems that can be found in various branches of human life. We offer to use the known approach based on the solution of direct and inverse dynamic problems. This approach us to define system motions by external signals that are given to it as well as define these signals by known motion trajectories. Since the used approach operates with the transfer functions apparatus we offer to generalize these functions by taking into account the system's non-zero initial state while performing the Laplace-Carson's transformation. Such an approach gives us the possibility to consider the generalized transfer function as some matrix differential operator that defines free and perturbed system motions. We study this operator in our paper and show the patterns of its determination and implementation. Our study allows us to supplement the definition of direct and inverse dynamic problems and consider the last one as the problem with several solutions that define the control signal, external efforts, and initial conditions. We use them to define the generalized direct and inverse transfer functions.]]>
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