Partial stability and boundedness of general dynamical systems on metric spaces

We develop new results for partial stability of invariant sets and boundedness of motions for dynamical systems defined on metric space using stability preserving mappings. Our results are applicable to a much larger class of systems than existing results, including dynamical systems that cannot be determined by the usual classical (differential) equations and inequalities. In contrast to existing results which pertain primarily to the analysis of equilibria, present results apply to invariant sets (including equilibria as a special case). We apply our results in the analysis of a class of discrete event systems (a computer load balancing problem). We are not aware of existing results on partial stability that apply to this class of systems. (C) 2002 Elsevier Science Ltd. All rights reserved.