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Some problems of discrete/continuous systems stabilization. (English) Zbl 1175.93185
The paper is devoted to the development of algebraic Kalman-like reachability and controllability criteria for linear periodic, time-invariant, discrete/continuous systems (DCS) and the solution of the eigenvalues assignment problem for linear time-invariant (LTI) DCS with available state-vector measurements. Continuous dynamics is described by ordinary differential equations with continuous control, and the discrete dynamics with discrete control excitations is described by difference equations for the system’s state jumps in prescribed time moments which specify the operating time of the discrete system. This class of models appeared previously by A. T. Barabanov and G. A. Agranovich [Din. Sist., Kiev 2, 17–24 (1983; Zbl 0532.49020)]. The transition matrices for the systems are investigated.

93D15 Stabilization of systems by feedback
93B05 Controllability
93B55 Pole and zero placement problems