Nabla derivatives associated with nonlinear control systems on homogeneous time scales

Abstract

The backward shift and nabla derivative operators, defined by the control system on homogeneous time scale, in vector spaces of one-forms and vector fields are introduced and some of their properties are proven. In particular the formulas for components of the backward shift and nabla derivative of an arbitrary vector field are presented.

Keywords

• nonlinear system
• time scale
• vector field
• one-form
• nabla and delta derivatives