Absolute stability of parametrically perturbed third-order systems

Abstract

Consideration was given to the behavior of the third-order systems in phase space. Regularities of motion of the phase trajectories were established, and a criterion for absolute nonoscillation was obtained. For the absolutely nonoscillatory systems, the Hurwitz conditions serve as the absolute stability criterion. For the oscillatory systems, an additional Bulgakov condition was introduced to eliminate the possibility of parametric resonance. This condition which is verified on the invariant set defined using the Poincare transform was shown to be a criterion for absolute stability of the oscillatory systems. The results obtained were used to solve the problem of absolute stability of a third-order control system with nonstationary sectorial nonlinearity.