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An approach for computing Lyapunov functions for nonlinear continuous-timedifferential equations is developed via a new, Massera-type construction. Thisconstruction is enabled by imposing a finite-time criterion on the integratedfunction. By means of this approach, we relax the assumptions of exponentialstability on the system dynamics, while still allowing integration over afinite time interval. The resulting Lyapunov function can be computed based onany K infinity function of the norm of the solution of the system. In addition,we show how the developed converse theorem can be used to construct an estimateof the domain of attraction. Finally, a range of examples from literature andbiological applications such as the genetic toggle switch, the repressilatorand the HPA axis are worked out to demonstrate the efficiency and improvementin computations of the proposed approach.

Computation of Lyapunov functions for nonlinear differential equations via a Massera-type construction