Conditions for stability and roughness of the distributed plant control system with a controller close to the degenerate system

Conditions for stability and roughness of a distributed plant control system with a controller close to the degenerate system (Schipanov's controller) were considered. The given operator relations between the plant output and controller are used for mathematical description of the plant and controller. For the linear plant, conditions were given for close-to-invariant behavior of the plant output. For the nonlinear control-linear plant, conditions for boundedness of the plant output, upper bound of the norm of the “action–output”, and the sufficient condition providing closeness of the output behavior to the invariant one were given.