This paper is concerned with the rigorous construction of hyperchaotic attractors in n-dimensional continuous-time systems. The method of analysis is based on the construction of a matrix controller and by using the standard dentition of Lyapunov exponents for an asymptotically stable limit set of the original system. The relevance of this approach is to show mathematically the possibility of c...

Closed-loop, asymptotically stable walking motions are designed for a 5-link, planar bipedal robot model with one degree of underactuation. Parameter optimization is applied to the hybrid zero dynamics, a 1-DOF invariant subdynamics of the full robot model, in order to create asymptotically stable orbits. Tuning the dynamics of this 1 DOF subsystem via optimization is interesting because asympt...

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 main goal of this paper is to prove that the global atractor of the equation ẋ(t) = −kx(t)+β tanh(x(t−r)) is an equilibrium point for any β such that |β| < k. Furthermore, we exhibit numerical evidences that the trivial solution is global asymptotically stable in all the region of the parameters where the equilibrium is local asymptotically stable.

The positive asymptotically stable continuous-time linear systems are approximated by corresponding asymptotically stable discrete-time linear systems. Two methods of the approximation are presented and the comparison of the methods is addressed. The considerations are illustrated by three numerical examples and an example of positive electrical circuit.

Based on the model provided by the Mulone and Straughan [1], we relax the population which are constant and obtain the drug-free equilibrium which is global asymptotically stable under some conditions. The system has only uniqueness positive endemic equilibrium which is globally asymptotically stable by using the second compound matrix.

This note examines stability properties of systems that result from switching among globally asymptotically stable nonlinear systems in triangular form. We show by means of a counterexample that, unlike in the linear case, such a switched system might not be globally asymptotically stable, uniformly over all switching signals. We then formulate conditions that guarantee this uniform global asym...

An epidemic model with incomplete treatment and vaccination for the newborns and susceptibles is constructed. We establish that the global dynamics are completely determined by the basic reproduction number R0. If R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable. If R0 > 1, the endemic equilibrium is globally asymptotically stable. Some numerical simulations are also ...