Stabilization of Nonlinear Systems with a Dither Control

摘要

A new approach is taken to analyze stabilization of a general nonlinear system with a dither input. Given the original system with a control, an autonomous relaxed system is constructed. It is shown that if the relaxed system is stable, then the original system with dither control would be stable in the finite time. An algorithm is given for constructing the dither control. The technique used here is general and does not have the limitations of the Dual Input Describing Function technique. Furthermore, in many cases it is possible to quarantee global contractive stability as well. Two examples are solved in detail using computer simulations for demonstration of the technique. (Author)