This note deals with the constant control problem for homogeneous cooperative and irreducible systems. These systems serve as models for positive systems. A necessary and sufficient condition for global asymptotic stability of the zero solution of this class of systems is known. Adding a constant control allows to shift the equilibrium point from zero to a point in the first orthant. We prove t...

This paper deals with the stability analysis of a simple metabolic system with feedback inhibition. The system is a sequence of monomolecular enzymatic reactions. The last metabolite acts as a feedback regulator for the rst enzyme of the pathway. The enzymatic reactions of the pathway satisfy MichaelisMenten kinetics. The inhibition is described by an hyperbolic model. Without inhibition, it is...

Abstract. In this paper, a predator-prey system with Holling type II functional response and stage structure is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is studied. The existence of the orbitally asymptotically stable periodic solution is established. By using suitable Lyapunov functions and the LaSal...

In this paper, delay-dependent stability analysis for neutral type neural networks with uncertain paramters and time-varying delay is studied. By constructing new Lyapunov-Krasovskii functional and dividing the delay interval into multiple segments, a novel sufficient condition is established to guarantee the globally asymptotically stability of the considered system. Finally, a numerical examp...

This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discrete-time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function. The developed converse Lyapunov theorem establishes existence of global Lyapunov functions for globally exponentially stable (GES) systems and for globally asymptotically stable systems, Lyapunov fun...

Given a globally asymptotically controllable system, we derive from an existence theorem of a semiconcave control-Lyapunov function, the construction of a globally asymptotically stable feedback in the Euler sense. The feedback is rather regular in the case of control systems affine in the control. Abridged English Version In this paper, we study systems of the general form ẋ(t) = f(x(t), u(t))...

We conduct rigorous stability analysis for the well-known cholera model proposed by Codeço [7]. Using theory of monotone dynamical systems, we prove that the endemic equilibrium, when it exists, of the model is globally asymptotically stable, implying the persistence of the disease in the absence of interventions. We then modify Codeço’s model by incorporating various control strategies, and st...

This paper is concerned with a cyclic predator-prey system with Sigmoidal type functional response. By using the differential inequality theory, some sufficient conditions are derived for the permanence of the system. By constructing a suitable Liapunov function, we obtain that the system has a unique asymptotically periodic solution which is globally asymptotically stable. Some numerical simul...

The goal of this paper is twofold. The first part presents a Lyapunov statement and proof of the concept of robust global practical exponential stability (RpGES) for nonlinear time varying systems. A RpGES-Lyapunov function for the overall system is exhibited. Its proof is a consequence of some results on converse Lyapunov theorems obtained by Tsinias in [19]. The second part provides sufficien...

In this paper the eeect of bounded input perturbation on the stability of nonlinear globally asymptotically stable delay diierential equations is analyzed. We investigate under which conditions global stability is preserved and if not, whether semi-global stabilization is possible by reducing the size of the perturbation or modifying its shape. This results in a general framework, in which the ...