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Inmany practical applications, studying the asymptotic stability of equilibriumpointsof a systemareof utmost importance. Furthermore, in some of such cases the response is restricted to only a sector of the state space. For example positive systems that are really common in chemical processes, have non-negativestate variables. For such systems stability analysis of the system using direct Lyapunov stability is not a suitable choice everywhen, since it suffices to consider of Lypunov conditions in a part of the state space that the existence of solutions is restricted to there andthe existence guarantee of at least a domain that includes the equilibrium point & has the Lypunov conditions, will not be required every time. In this paper a new notion of stability which is called corner stability is defined which is more suitable for studying asymptotic stability of equilibriumpoints in such systems.To derive the sufficient condition of corner stability a theorem is stated in this paper, and fortwo different cases studiescorner stability ofanequilibrium pointattheorigin, is studied according to this theorem.

Keywords: Autonomous systems, positive system, stability analysis, Lyapunov stability, asymptotic stability

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