Stability of nonlinear systems with nonunique equilibrium position

The object of study is systems with nonunique equilibrium position described by nonlinear differential equations with discontinuous right-hand members. By using the second method of Liapunov and the solution of quadratic matrix inequalities, one obtains sufficient, and in some cases necessary, conditions for different types of stabilities of the sets of equilibrium states. These conditions are in frequency form and are used to study a number of nonlinear automatic control systems with dead zones, gyroscopic systems with Coulomb friction, and electronic phase synchronization systems.