In this paper, a generalized mathematical model of spread of infectious disease as SIRS epidemic model is considered as a nonlinear system of differential equation. We prove that for positive initial conditions the resulting equivalence system has positive solution and under some hypothesis, this system with initial positive condition, has a positive $T$-periodic solution which is globally asym...

A complete stability analysis is performed on a planar discrete-time system of the form ( +1) = sat( ( )), where is a Schur stable matrix and sat is the saturation function. Necessary and sufficient conditions for the system to be globally asymptotically stable are given. In the process of establishing these conditions, the behaviors of the trajectories are examined in detail.

A type of delayed Lotka-Volterra competition reaction-diffusion system is considered. By constructing a new Lyapunov function, we prove that the unique positive steady-state solution is globally asymptotically stable when interspecies competition is weaker than intraspecies competition. Moreover, we show that the stability property does not depend on the diffusion coefficients and time delays.

We consider continuous time nonlinear time varying systems that are globally asymptotically stabilizable by state feedbacks. We study the stability of these systems in closed loop with controls that are corrupted by both delay and sampling. We establish robustness results through a Lyapunov approach of a new type.

The nonlinear feedback cascade model of the underactuated IWP is obtained through a collocated partial feedback linearization and a global change of coordinates. A nonlinear controller is designed with the nonlinear recursive technology. The system stability is proved with Lyapunov theory. The simulation results show the system is globally asymptotically stable to the origin.

In this paper, we consider a delayed diffusive Leslie–Gower predator–prey system with homogeneous Neumann boundary conditions. The stability/instability of the coexistence equilibrium and associated Hopf bifurcation are investigated by analyzing the characteristic equations. Furthermore, using the upper and lower solutions method, we give a sufficient condition on parameters so that the coexist...

This paper presents a converse Lyapunov theorem for discrete-time systems with disturbances taking values in compact sets. Among several new stability results, it is shown that a smooth Lyapunov function exists for a family of time-varying discrete systems if these systems are robustly globally asymptotically stable. c © 2002 Elsevier Science B.V. All rights reserved.

It is known that many discrete time recurrent neural networks, such as e.g. neural state space models, multilayer Hoppeld networks and locally recurrent globally feedforward neural networks, can be represented as NL q systems. Suucient conditions for global asymptotic stability and input/output stability of NL q systems are available, including three types of criteria: diagonal scaling and crit...

Stability and performance of networked control systems has been a recent area of interest in the control literature. The inclusion of a shared communication network between plant and controller inevitably leads to occasional random data loss. We provide novel results relating to the probability of such a system being globally asymptotically stable or input to state stable. Copyright c ©2005 IFAC

We present constructions of a local and global common Lyapunov function for a finite family of pairwise commuting globally asymptotically stable nonlinear systems. The constructions are based on an iterative procedure, which at each step invokes a converse Lyapunov theorem for one of the individual systems. Our results extend a previously available one which relies on exponential stability of t...