We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are uniformly globally asymptotically stable. This leads to new sufficient conditions for uniform global exponential, uniform globa...

The paper presents the vector-host disease with a variability in population. We assume, the disease is fatal and for some cases the infected individuals become susceptible. We first show the local and global stability of the disease-free equilibrium, for the case when R 0 < 1. We also show that for R 0 < 1, the disease free-equilibrium of the model is both locally as well as globally stable. Fo...

If one can find a control Lyapunov function (CLF) for a given nonlinear system, the control input stabilizing the system can be easily obtained. To find a CLF, the time derivative of an energy function should be negative definite. This procedure frequently requires a control input which is a rational function or includes an inverse function. The control input is not defined on the specific stat...

We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are uniformly globally asymptotically stable. This leads to new sufficient conditions for uniform global exponential, uniform globa...

A general disease transmission model of SIRS type is formulated and analyzed. There is constant recruitment into the susceptible class, mass action incidence, and stage age in the removed class. Disease fatalities occur in the infective class and the removed stages. Sufficient conditions are given for the endemic equilibrium to be globally asymptotically stable. For example, if the disease conf...

Here, we study the ultimately bounded stability of network of mismatched systems using Lyapunov direct method. We derive an upper bound on the norm of the error of network states from its average states, which it achieves in finite time. Then, we devise a decentralized compensator to asymptotically pin the network of mismatched systems to a desired trajectory. Next, we design distributed estima...

Sliding mode control synthesis is developed for a class of uncertain time-delay systems with nonlinear disturbances and unknown delay values whose unperturbed dynamics is linear. The synthesis is based on a new delay-dependent stability criterion. The controller constructed proves to be robust against sufficiently small delay variations and external disturbances. An admissible upperbound such t...

*Correspondence: [email protected] School of Mathematics and Computer Science, Shanxi Normal University, Linfen, P.R. China Abstract In this paper, we study a new SEIRS epidemic model describing nonlinear incidence with a more general form and the transmission of influenza virus with disease resistance. The basic reproductive number 0 is obtained by using the method of next generating matrix. ...

A differential electronic Susceptible-Infectious-RemovedSusceptible (e-SIRS) epidemic model of virus and worms in a computer network has been formulated. Latent period, immune period and time for self replication have been considered. Stability of the result is stated in terms of the threshold parameter. We have derived an explicit formula for the reproductive number and have shown that the vir...

This paper is concerned with the existence, uniqueness and globally asymptotic stability of traveling wave fronts in the quasi-monotone reaction advection diffusion equations with nonlocal delay. Under bistable assumption, we construct various pairs of superand subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing trav...