Partial stability and boundedness of general dynamical systems on metric spaces
The authors develop a comparison theory for the partial stability of invariant sets and for the boundedness of motions for dynamical systems on metric spaces. To accomplish this, they utilize mappings from the dynamical system under study to a well understood comparison system which preserve the stability and boundedness properties. The results are applicable to a wide class of dynamical systems including some systems that cannot be determined by classical differential equations or inequalities. Moreover, the results are not only applicable to the analysis of equilibria but also to invariant sets. The theory is applied to the analysis of a class of discrete event systems, in particular, a computer network load balancing problem.
scientific article; zbMATH DE number 1880009