Uniform Ultimate Boundedness of Probe-to-Probe Dynamics in Dual Probe Atomic Force Microscopy

Atomic force microscopes use a probe to interface with matter at the nanoscale through a variety of imaging or manipulation methods. A dual-probe atomic force microscope (DP-AFM) has been proposed for simultaneous imaging and manipulation. One challenge of DP-AFM is probe-to-probe contact, which may occur intentionally such as when locating one probe with the other. This work studies the stability for such interactions where the 1^st probe is in the tapping mode (typically used for imaging) and 2^nd probe is in the contact mode (typically used for manipulation). A state dependent switched model is proposed for DP-AFM. A theorem is proposed for uniformly ultimately bounded (UUB) stability of switched systems under a sequence nonincreasing condition and applied to the DP-AFM problem.