Qualitative analysis and estimation of linearization error for multiply connected dynamical systems

Multiply connected dynamical systems described by nonlinear finite-dimensional differential equations are considered. Conditions of asymptotical stability with respect to one part phase variables and conditions of uniform boundedness with respect to another part phase variables are suggested. Estimation of linearization error is constructed by the aid of Lyapunov vector functions method. The obtained results can be used in problems of analysis of behavior of technical manipulators. In the present paper a constructive method of qualitative analysis of dynamical systems multiply, as well as a method of constructing estimates linearization of these systems. The results obtained are solving problems of correctness of the use of linearized systems in the theory of motion stability of nonlinear systems.