In this work, we reexamine the time scale Laplace transform as defined by Bohner and Peterson [M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, BirkhÃ¤user,â€¦ (More)

We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time scales.â€¦ (More)

2011 IEEE 43rd Southeastern Symposium on Systemâ€¦

2011

For LTI systems on a class of nonuniform discrete domains, we establish a region in the complex plane for which pole placement is a necessary and sufficient condition for exponential stability ofâ€¦ (More)

We consider the dynamics of a dark soliton in an elongated harmonically trapped Bose-Einstein condensate. A central question concerns the behavior at finite temperatures, where dissipation arises dueâ€¦ (More)

2010 42nd Southeastern Symposium on System Theoryâ€¦

2010

A fundamental result in linear system theory is the development of a linear state feedback stabilizer for time-varying systems under suitable controllability constraints. This result was previouslyâ€¦ (More)

Above a critical velocity, the dominant mechanism of energy transfer between a moving object and a dilute Bose-Einstein condensate is vortex formation. In this paper, we discuss the critical velocityâ€¦ (More)

Vortices are pervasive in nature, representing the breakdown of laminar fluid flow and hence playing a key role in turbulence. The fluid rotation associated with a vortex can be parameterized by theâ€¦ (More)