Shram V. Sets of robust stability and stabilization of families of dynamical systems

In the thesis, new constructive methods for robust stability investigation and robust stabilization of motion of mechanical systems described by differential and difference vector-matrix type systems are developed. Stability, asymptotic stability and instability conditions for the second order differential systems with polyhedral uncertain matrix coefficients are constructed. New algebraic conditions for robust absolute stability of linear time delay systems and asymptotical mean-square stability of stochastic Ito systems with uncertain coefficients are established. A general class of matrix inequalities with polyhedral matrix coefficients which equivalent to the consistency of finite systems of matrix inequalities is distinguished. Sets of robust asymptotical stability of the zero solution of nonlinear differential systems are constructed. The developed research methods are applied in the stability and stabilization of motion problems for mechanical systems with uncertain parameters (rotor system, double inverted pendulum on a card, active suspension of a car seat etc.).