On the qualitative behaviors of solutions of third order nonlinear differential equations

We present some new results about oscillation and asymptotic behavior of solutions of third order nonlinear differential equations of the form

(r₂(t)(r₁(t)y^′)^′)^′+p(t)y^′+q(t)f(y(g(t)))=0.     

Stability and synchronization for Markovian jump neural networks with partly unknown transition probabilities

This paper addresses the problems of stability and synchronization for a class of Markovian jump neural networks with partly unknown transition probabilities. We first study the stability analysis problem for a single neural network and present a sufficient condition guaranteeing the mean square asymptotic stability. Then based on the Lyapunov functional method and the Kronecker product technique, the chaos synchronization problem of an array of coupled networks is considered. Both the stability and the synchronization conditions are delay-dependent, which are expressed in terms of linear matrix inequalities. The effectiveness of the developed methods is shown by simulation examples.     

Stability analysis for discrete delayed Markovian jumping neural networks with partly unknown transition probabilities

This paper addresses the analysis problem of asymptotic stability for a class of uncertain neural networks with Markovian jumping parameters and time delays. The considered transition probabilities are assumed to be partially unknown. The parameter uncertainties are considered to be norm-bounded. A sufficient condition for the stability of the addressed neural networks is derived, which is expressed in terms of a set of linear matrix inequalities. A numerical example is given to verify the effectiveness of the developed results.     

Sliding mode control for polytopic differential inclusion systems

The stabilization problem of polytopic differential inclusion (PDI) systems is investigated by using sliding mode control. Sliding surface is designed and sufficient conditions for asymptotic stability of sliding mode dynamics are derived. A novel feedback law is established to make the state of system reach the sliding surface in a finite time. Finally, an example is given to illustrate the validity of the proposed design.     

Oscillations and transfer properties of relay feedback systems with time-delay linear plants

Oscillations and transfer properties of relay feedback systems with linear plants having a dead time (time delay) are considered. Poincare maps are found explicitly in terms of the system parameters. The oscillatory and transfer properties are presented in the format of the locus of a perturbed relay system (LPRS), which represents the continuum of all possible periodic solutions and transfer properties of the system with a given linear plant. Conditions of local orbital asymptotic stability are found in terms of the system parameters. The proposed approach is illustrated by examples.     

A bootstrap goodness of fit test for the generalized Pareto distribution

This paper proposes a bootstrap goodness of fit test for the Generalized Pareto distribution (GPd) with shape parameter γ. The proposed test is an intersection–union test which tests separately the cases of γ≥0 and γ<0 and rejects if both cases are rejected. If the test does not reject, then it is known whether the shape parameter γ is either positive or negative. A Monte Carlo simulation experiment was conducted to assess the power of performance of the intersection–union test. The GPd hypothesis was tested on a data set containing Mexico City’s ozone levels. ¹     

Vision-based control for rigid body stabilization

This paper addresses the problem of stabilizing to a desired equilibrium point an eye-in-hand system, which consists of a single camera mounted on a rigid body free to move on . It is assumed that there is a collection of landmarks fixed in the environment and that the image coordinates of those landmarks are provided to the system by an on-board CCD camera. The proposed method addresses not only the problem of stabilization but also that of maintaining feature visibility along the system’s trajectory. The resulting solution consists of a feedback control law based on the current and desired image coordinates and reconstructed attitude and depth ratio information, which guarantees that (i) the desired equilibrium point is an almost global attractor; (ii) a set of necessary conditions for feature visibility holds throughout the system’s trajectories; and (iii) the image of a predefined feature point is kept inside the camera’s field of view.