The Perturbed Motions of Interval Time-Variant Dynamical System

The paper is devoted to developing the theoretic backgrounds to study nonlinear time-variant system motions. To develop these backgrounds, we use interval methods and define motion trajectories in the boundaries of the interval of possible system motions. The above-mentioned trajectories are found by using piece-wise linear boundaries for nonlinear functions. We consider these boundaries as tangent and secant lines for the case of a one-variable nonlinear function. In the case of a multivariable function, the boundaries are defined as the piece-wise continuous planes. One can find parameters of the piece-wise linear functions, which bounds the considered nonlinearities, by combining the analytical geometry approaches with optimal methods. Such an approach allows us to minimize the square/volume of subdomains, where the nonlinear functions of single/multi variables are defined. In the most general case when time-variant dynamical system is studied, one can use as the arguments for the above-mentioned functions both systems state variables and time. This fact gives us the possibility to write down system boundary dynamics in a form similar to linear ordinary differential equations but with piece-wise continuous factors. We use these equations to define the perturbed motion equations which show variations between the considered system motions and the desired one.