Global nonlinear dynamics of various classes of closed loop attitude control systems have been studied in recent years [1]. Closely related results on attitude control of a spherical pendulum (with attitude an element of the twosphere S2) and of a 3D pendulum (with attitude an element of the special orthogonal group SO(3)) are given in [2], [3]. These publications address the global closed dyna...

The following conjecture of M. L. Zeeman is proved. If three interacting species modeled by a competitive Lotka–Volterra system can each resist invasion at carrying capacity, then there can be no coexistence of the species. Indeed, two of the species are driven to extinction. It is also proved that in the other extreme, if none of the species can resist invasion from either of the others, then ...

In this work we prove the necessity of the existence of a density function for a globally asymptotically stable dynamical system.

A continuous-time SIV (susceptible-infected-vaccinated) model of the transmission of Gonorrhea among homosexuals is analyzed. A basic reproduction number Ro is identified and it is shown that the disease-free equilibrium is globally asymptotically stable when Ro ≤ 1. It is also shown that this equilibrium is unstable when Ro > 1 and there exists a globally asymptotically stable endemic equilibr...

We show that a nonlinear locally uniformly asymptotically stable infinite-dimensional system is automatically locally input-to-state stable (LISS) provided the nonlinearity possesses some sort of uniform continuity with respect to external inputs. Also we prove that LISS is equivalent to existence of a LISS Lyapunov function. We show by means of a counterexample that if this uniformity is not p...

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...

In this paper we present a robust hybrid motion/force controller for rigid robot manipulators. The main contribution of this paper is that the proposed hybrid control system is able to accomplish motion objectives in free directions and force objectives in constrained directions under parametric uncertainty both in robot dynamics and stiffness constraint constant. Also, the given scheme is prov...

We study the SIR epidemic model with varying total population size and constant immigration rate. We derive the sufficient conditions on parameters of the system to guarantee that the equilibrium points of the system are locally asymptotically stable or globally asymptotically stable. If the disease-free equilibrium point is stable, then the disease will not affect the population in the system....

Sufficient conditions are given which guarantee that the trivial solution x = 0 for a nonlinear integro–differential system is globally attracting. As an example, this result is applied to a SIRS epidemic model with subpopulations to show that, under certain conditions, the endemic equilibrium is globally asymptotically stable.

A model with differential susceptibility, differential infectivity (DS-DI), and age of infection is formulated in this paper. The susceptibles are divided into n groups according to their susceptibilities. The infectives are divided into m groups according to their infectivities. The total population size is assumed constant. Formula for the reproductive number is derived so that if the reprodu...