This issuePrevious ArticleControl of synchrony by delay coupling in complex networksNext ArticleInvariant feedback design for control systems with lie symmetries - A kinematic car example
Some implications of a new approach to exponential functions on time scales
We present a new approach to exponential functions on time scales
and to timescale analogues of ordinary dierential equations. We describe in
detail the Cayley-exponential function and associated trigonometric and hyperbolic
functions. We show that the Cayley-exponential is related to implicit
midpoint and trapezoidal rules, similarly as delta and nabla exponential functions
are related to Euler numerical schemes. Extending these results on any
Padé approximants, we obtain Pade-exponential functions. Moreover, the exact
exponential function on time scales is defined. Finally, we present applications
of the Cayley-exponential function in the $q$-calculus and suggest a general
approach to dynamic systems on Lie groups.