Stability research of a three-dimensional controlled system by the first Lyapunov method and the bifurcational picture of field states

Stability analysis of three-dimensional controlled system with logic controller is carried out. Interaction of logic controller with control object is represented in the form of rules of view: if ... then. The part «if» means coupling of logic operations, and part «then» represents controlling influence on the control object. For research of stability it is used spectrally-bifurcational method which is based on combined using of the first Lyapunov method and a bifurcational picture of field states of system. Stability stocks of three types are defined for studied system. Computer modeling is carried out and phase portraits are constructed. The obtained results can be used for the solution of problems of designing of logic controllers, problems of stability and stabilization, and also for design of technical control systems.