By constructing the Lyapunov Krasovskii functional appropriately, we can avoid the supplementary requirement that the time-derivative of time-varying delay must be smaller than one.
It is shown by constructing the objective functional given by the total square of the difference between predictions from the BJKCA interaction model and experimental data obtained with transmitted USW that the inverse problem is ill-posed, since the functional exhibits several local minima and maxima.
By constructing the Lyapunov functional, the exponential synchronization criteria dependent on diffusion coefficients, diffusion space, stochastic perturbation and control width were obtained.
If the basic reproduction number is less than 1, then the viral-free steady state (E_{0}) is globally asymptotically stable, which is proved by fluctuation lemma and comparison method; if (mathcal {R}_{0}>1) is greater than 1, the endemic steady state (E^) is globally asymptotically stable, which is proved by constructing the Lyapunov functional.
By constructing the Lyapunov functionals, the threshold conditions on the global stability of the infection-free, immune-free and interior equilibria are established if the space is assumed to be homogeneous.
By constructing the Lyapunov Krasovskii functional, we prove the asymptotical stability of the closed-loop system.
By constructing the appropriate Lyapunov Krasovskii functional using the available information about the actual sampling pattern, a new set of sufficient condition is obtained to guarantee that the singular networked cascade control systems to be admissible and strictly (Q,S,R -dissipative.
In Section 3, the main results of global robust exponential synchronization are obtained by constructing the appropriate Lyapunov functional and applying inequality skills.
We have established a new sufficient condition which includes the diffusion coefficients by constructing the suitable Lyapunov functional, introducing many real parameters and applying inequality techniques.
After that, Kim got a more exact condition by constructing the modified Lyapunov-Razumikhin functionals [22].
