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Approaches to estimating for the number of almost periodic solutions of ordinary differential equations are considered. Conditions that allow determinating both the upper and lower bounds for these solutions are found. The existence and stability of almost periodic problems are considered. [ABSTRACT FROM AUTHOR]

The theory of derived numbers is developed and the way to use it in the study of nondifferentiable functions behavior is presented. [ABSTRACT FROM AUTHOR]

In this article the authors prove the theorems giving the necessary and sufficient conditions for stability of robotic and mechatronic systems motion in terms of Lyapunov functions theory with the use of set-theoretic approach. [ABSTRACT FROM AUTHOR]

The Fermat, Roll and Lagrange theorems are generalized into the class of nondifferentiable functions, the necessary and sufficient conditions for monotonicity and convexity of one variable functions are given. [ABSTRACT FROM AUTHOR]

In this paper the stabilization problems of program motion of objects with elastically connected elements are considered. The conditions for stabilizing a program motion x=0 of the control object are given. [ABSTRACT FROM AUTHOR]

In the paper the authors propose a method of bilateral control for space robotic manipulators construction with large delays in transmissions of control signals from the Earth to the local space manipulator’s control system. [ABSTRACT FROM AUTHOR]

In this paper the problems of stability and asymptotic stability conditions for the motion of mechanical systems with holonomic and non-holonomic constraints are under consideration. Stability analysis for the systems of differential equations is given in term of the second Lyapunov’s method. With the use of the set-theoretic approach the necessary and sufficient conditions for stability and asymptotic stability of zero solution of the considered system are formulated. [ABSTRACT FROM AUTHOR]

The article presents analysis on construction of two-stage remote control for space robots. This control ensures efficiency of the robot control system at large delays in transmission of control signals from the ground control center to the local control system of the space robot. The conditions for control stability of and high transparency are found. [ABSTRACT FROM AUTHOR]

The paper deals with first-order differential equations under the assumption that the right-hand side is a periodic function of time and continuous in the set of arguments. Pliss V.A. obtained the first results for a particular class of equations and showed that a number of theorems can not be continued. In this paper, it was possible to reduce the restrictions on the degree of smoothness of the right-hand side of the equation and obtain upper and lower bounds on the number of possible periodic solutions. [ABSTRACT FROM AUTHOR]

In this paper both scalar and vector controls are built which solve the problem of relay-stabilizing of the system with hysteresis type nonlinearities. The behavior of closed system solutions in a neighborhood of its invariant set is studied, its structure is researched. [ABSTRACT FROM AUTHOR]