Chirayu D. Athalye

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In this paper, we give the complete characterization of all possible Lyapunov functions for the specific autonomous system ẋ=-x. This characterization is in terms of strict quasi-convexity of a Lyapunov candidate at the equilibrium point, and it is in a way independent of system dynamics. From Lyapunov theory it is well known that, a continuously(More)
In this paper, we analyze the `2-stability and the `∞-stability of general discrete 2-D autonomous systems. The problem of `∞-stability has not been studied before for general 2-D autonomous systems. We give a necessary condition for the `∞-stability of discrete 2-D autonomous systems. We also give sufficient conditions for the `2-stability and the(More)
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