Slyn'ko V. Motion stability of mechanical systems: hybrid models

In the dissertation a series of problems on stability of stationary motions are solved for the mechanical systems with impulsive effects, continuous-discrete mechanical systems and systems under incomplete information conditions. For the mechanical systems with impulsive effects generalization of theorems of the direct Liapunov method based on two auxiliary functions is proposed along with new methods of constructing piecewise differentiable Liapunov functions for linear and essentially nonlinear systems. Conditions of Liapunov stability and practical stability of motion are obtained for quasilinear mechanical systems with discrete regulator. A problem on dynamic impulse stabilization of stationary rotation of a dynamically symmetric rigid body on a string suspension is solved. Asymptotic stability conditions for linear hybrid system of perturbed motion differential equations with distributed component are established in terms of the method of constructing the matrix-valued Liapunov functional proposed in the dissertation. For the mechanical systems under incomplete information conditions a mathematical model is constructed in the form of fuzzy differential equation.