Abstract
The necessary and sufficient conditions for accurate construction of a Lyapunov function and the necessary and sufficient conditions for a set to be the asymptotic stability domain are algorithmically solved for a nonlinear dynamical system with continuous motions. The conditions are established by utilizing properties of o‐uniquely bounded sets, which are explained in the paper. They allow arbitrary selection of an o‐uniquely bounded set to generate a Lyapunov function.Simple examples illustrate the theory and its applications.
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