An introduction to product integration on time scales

Abstract

This paper represents a short survey of product integration on time scales. We introduce the notion of product delta-integral of a matrix function defined on an arbitrary time scale, and thus generalize the classical definition of product integral.

We summarize its properties and describe its relation to linear systems of dynamic equations. Finally, we generalize the notion of the matrix exponential function.

Keywords

• product integral
• matrix exponential
• linear dynamic system
• regressive function