The Development of Mathematical Modeling for Solving Problem of Assessment of the Stability of Nonlinear Systems with Slowly Changing Parameters

摘要

The major objective of this study is to obtain mathematical models for evaluation behavior of non-linear system, parameters non-linear elements are taken to be time change. The problem is solved by transaction from description at non-linear non-stationary system in space of variable states to description of its behavior in space of parameter increments by means of apparatus of Sensitivity functions. Using this apparatus, we transit from non-linear differential equation, to describing behavior system as a space of variable states to linear description at the systems increment change at these parameters. For overcoming the generalized functions which appear invariably during obtaining the sensitivity function, we used describing function. The main study also is to develop a mathematical model to estimate the stability of electric drive relay action and to identify areas of its robust stability when exposed to uncontrolled parametric perturbations described by harmonic laws.