Synthesis of simple relay controllers in self-oscillating control systems

We consider the problem of synthesizing simple structured relay controllers as part of a self-oscillatory system with a linear plant. The controller structure is said to be simple if it cannot be simplified since any further simplification that consists in excluding any element from it leads to the impossibility of satisfying all the requirements for the system. It is necessary to ensure the presence of self-oscillations with a given frequency and amplitude in the system and bring its behavior closer to the desired one. A method for solving the problem under consideration is proposed.