Floquet Theory for Stability of Differential Algebraic Equations.

Abstract

Motivated by a great useful of some types of non autonomous differential algebraic
 equation systems ( so called strangeness free ) and its applied in different scientific
 fields, we present several new results for studying such systems by classical Floquet
 Theory, which we extended from linear periodic ordinary differential equation systems
 into linear periodic differential algebraic equation systems. For both systems we
 investigate that they have the same Floquet exponents. The relation between monodromy
 matrices of both systems is also presented. Classification of solution according to the
 nature of Floquet exponent is established. Then according to these results, we study the
 stability and bifurcation phenomenon of our differential algebraic equation systems.