Stabilité de systèmes différentielles implicites dans les espaces de Hilbert

Abstract

The study of a bundle (Regelier and singular) of matrices can be generalized for a bundle of operators in Hilbert spaces. The spectral daisy theory of operator in spaces of infinite dimension admits applications in physics for example the theory of stability of some systems dynamics and generalization of Liapouov's theorem. This thesis consists of an introduction and four (04) chapters and finally a bibliographic list of 19 titles. In the first chapter we recall the basic tools on the spectral theory, aunsi some definitions on sheaf of matrices The second chapter is devoted to some methods of solving systems finite-dimensional linear differentials. The third chapter on the notion of the stability of these systems in finite dimension and infinite, In the last chapter is devoted to the spectral decomposition of a bundle of operators thus generalizes the classical Liapunov theorem used to stability theory explicit systems in infinite dimension to a bundle of operators (the study of implicit homogeneous system stability).