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A new type of stability is introduced and its equivalent Lyapunov characterization is presented. The problem of global stability for the compact set composed of all invariant solutions of a nonlinear system (several equilibriums, for instance) is studied. Such problem statement allows us to analyze global stability properties for multi-stable systems. It is shown that several well-known multi-stable systems satisfy this new stability property. GLOBAL LYAPUNOV ANALYSIS OF MULTI-STABLE NONLINEAR SYSTEMSdoi:10.1137/090767509 fatcat:lwxlbrol6fd43aqsomyru7m5di