Stability of differential inclusions defined by locally Lipschitz compact valued maps is addressed. It is shown that if such a differential inclusion is globally asymptotically stable, then in fact it is uniformly globally asymptotically stable (with respect to initial states in compacts). This statement is trivial for differential equations, but here we provide the extension to compact (not ne...

In this paper, we consider global asymptotic properties for an age-structured model of heroin use based on the principles of mathematical epidemiology where the incidence rate depends on the age of susceptible individuals. The basic reproduction number of the heroin spread is obtained. It completely determines the stability of equilibria. Using the direct Lyapunov method with Volterra type Lyap...

ABSTRACT. For a class of multigroup SIR epidemic models with varying subpopulation sizes, we establish that the global dynamics are completely determined by the basic reproduction number R0. More specifically, we prove that, if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable; if R0 > 1, then there exists a unique endemic equilibrium and it is globally asymptotically ...

Stability A globally asymptotically stable equilibrium is a state with the property that all solutions converge to this state, with no large excursions. Stabilization A system is stabilizable (with respect to a given state) if it is possible to find a feedback law that renders that state a globally asymptotically stable equilibrium. Lyapunov and control-Lyapunov functions A controlLyapunov func...

Abstract. A mathematical model describing the transmission dynamics of an infectious disease with an exposed (latent) period, relapse and a saturation incidence rate is investigated. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is established. By using suitable Lyapunov functionals and LaSalle’s invariance ...

In this paper, the sliding mode observers design techniques for MIMO and as a simple example for SISO systems are systematically advanced as a first purpose. Design parameters are selected such that on the defined switching surface always is generated asymptotically stable sliding mode. Moreover, observer state error dynamics is globally robustly asymptotically stable. Then, advanced design tec...

A multi-stage model of disease transmission, which incorporates a generalized non-linear incidence function, is developed and analysed qualitatively. The model exhibits two steady states namely: a disease-free state and a unique endemic state. A global stability of the model reveals that the disease-free equilibrium is globally asymptotically stable (and therefore the disease can be eradicated)...

We extend a recent investigation by Meehan et al. (2017) [1] regarding the global stability properties of the general Kermack-McKendrick model to the multi-strain case. We demonstrate that the basic reproduction number of each strain R0j represents a sharp threshold parameter such that when R0j ≤ 1 for all j each strain dies out and the infection-free equilibrium is globally asymptotically stab...

The Popov criterion is applied to control system analysis and design. Nonlinear dynamic compensators (NDC) are int reduced which ensure absolute stability without penalizing the available feedback. 1 Multiwindow Controllers and Nonlinear Dynamic Compensation Ivlultiwindow controllers consisting of linear controllers with nonlinear windows [1,2] perform superior to linear controllers. They can b...

In chaos synchronization, the main goal is to design such controller(s) that synchronizes the states of master and slave system asymptotically globally. This paper studied and investigated the synchronization problem of two identical Chen, and identical Tigan chaotic systems and two non-identical Chen and Tigan chaotic systems using Non-linear active control algorithm. In this study, based on L...