On the issue of control of neutral-type systems by hybrid controllers with state feedback

For linear autonomous systems of neutral type, an approach to control design problems in the form of feedback based on a new class of hybrid controllers is proposed. The structure of hybrid regulators necessarily includes a differential equation, so the closed system becomes differential-algebraic. A distinctive feature of hybrid controllers is the existence of elementary transformation of equations of a closed-loop system, which make it possible to obtain an independent subsystem of neutral type. In this case, the specified subsystem of neutral type uniquely determines the behavior of the solution $x(t)$ of the original open-loop system (possibly as a vector component of the solution vector of the closed-loop system). The main advantages of using hybrid controllers include the possibility of their application to systems that do not satisfy the “traditional” controllability properties. The properties of hybrid controllers have been studied. The author gives an example of using these controllers to solve a new problem of controlling the coefficients of a characteristic quasi-polynomial in the case where the approaches known in the literature are not applicable. The possibility of using hybrid controllers to solve the $0$-controllability problem using the finite control method is demonstrated.