Asymptotic stability in general dynamical systems

Abstract

GENERAL dynamical systems are used to describe multivalued (contingent) differential equations [5, 18, 191, differential equations without uniqueness [21], control systems [l, 5, 8, 9, 11, 14, 231 and functional differential equations [ 131. Alternative names for general dynamical systems are used in the literature. Among them are set-valued dynamical systems 114). dispersive dynamical systems [22] and dynamical polysystems [l]. Pelczar [15] and Sobanski [20] among others in the Polish school considered the so-called generalized pseudo-dynamical systems which are basically generated dynamical systems without any continuity assumptions on the attainability maps. Before going further in our analysis, let us pause for a moment to give the definition of a general dynamical system that will be used here.