Computation of Lyapunov functions for nonlinear differential equations via a Yoshizawa—type construction

An approach for computing Lyapunov functions for nonlinear continuous-time differential equations is developed via an alternative Yoshizawa-type construction. This construction is enabled by imposing a finite-time criterion on the integrated function. By means of this approach, we relax the assumption of exponential stability on the system dynamics, while still allowing computation over a finite time interval. The resulting Lyapunov function can be computed based on any K∞-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 estimate of the domain of attraction. Finally, some examples are worked out to demonstrate the efficiency and improvement in computations of the proposed approach.