@article{pandey_converse_nodate,
	title = {On a {Converse} {Theorem} for {Finite}-{Time} {Lyapunov} {Functions} to {Estimate} {Domains} of {Attraction}},
	abstract = {The main result of the paper is a new converse theorem for finite-time Lyapunov functions. We show the existence of a finite-time Lyapunov function for an autonomous continuoustime nonlinear dynamical system if the origin of the system is asymptotically stable. Our proof extends the recent results in finite-time Lyapunov function theory by providing an alternative converse proof for the existence of finite-time Lyapunov functions. In particular, we show that given asymptotic stability of the origin, the linearized dynamics satisfy global finitetime Lyapunov function conditions hence proving the converse theorem. Using our results, we present a consolidated theory for using and constructing Lyapunov functions to certify system stability properties. We also propose a constructive algorithm to efficiently compute non-conservative estimates of the domain of attraction for nonlinear dynamical systems.},
	language = {en},
	author = {Pandey, Ayush and Ames, Aaron D},
	pages = {7},
}

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