Sylvester’s Matrix Equation in the Problem of the Direct Synthesis of Stabilizing Feedback of a Linear Discrete-Time Stationary System Based on the Data on Its States

This paper presents a solution of the problem of designing a stabilizing state feedback for a linear multivariable discrete-time stationary system based on the data of the system’s behavior. It is assumed that the system’s matrices are unknown. An algorithm for directly designing a feedback matrix based on the Sylvester matrix equation without solving the identification problem is considered. The conditions for the existence of a solution of the design problem are obtained. A numerical example is considered.