Continuous finite-time state feedback stabilizers for some nonlinear stochastic systems

This paper is concerned with the problem of finite-time stabilization for some nonlinear stochastic systems. Based on the stochastic Lyapunov theorem on finite-time stability that has been established by the authors in the paper, it is proven that Euler-type stochastic nonlinear systems can be finite-time stabilized via a family of continuous feedback controllers. Using the technique of adding a power integrator, a continuous, global state feedback controller is constructed to stabilize in finite time a large class of two-dimensional lower-triangular stochastic nonlinear systems. Also, for a class of three-dimensional lower-triangular stochastic nonlinear systems, a recursive design scheme of finite-time stabilization is given by developing the technique of adding a power integrator and constructing a continuous feedback controller. Finally, a simulation example is given to illustrate the theoretical results. © 2014 John Wiley & Sons, Ltd.

Some properties of finite-time stable stochastic nonlinear systems

In this paper we study some properties of finite-time stable stochastic nonlinear systems. We begin by showing several continuous dependence theorems of solutions on initial values under some conditions on the coefficients of stochastic systems. We then derive some regular properties of its stochastic settling time for a finite-time stable stochastic nonlinear system. We show continuity, positive definiteness and boundedness of the expected stochastic settling time under appropriate conditions. Finally, a Lyapunov function is constructed by making use of the expectation of the stochastic settling time, and the infinitesimal generator of the stochastic system defined on the Lyapunov function is also given, and hence resulting in a converse Lyapunov theorem of finite-time stochastic stability.

Nonparametric rank tests for non-stationary panels

We develop a set of nonparametric rank tests for non-stationary panels based on multivariate variance ratios which use untruncated kernels. As such, the tests do not require the choice of tuning parameters associated with bandwidth or lag length and also do not require choices with respect to numbers of common factors. The tests allow for unrestricted cross-sectional dependence and dynamic heterogeneity among the units of the panel, provided simply that a joint functional central limit theorem holds for the panel of differenced series. We provide a discussion of the relationships between our setting and the settings for which first- and second generation panel unit root tests are designed. In Monte Carlo simulations we illustrate the small-sample performance of our tests when they are used as panel unit root tests under the more restrictive DGPs for which panel unit root tests are typically designed, and for more general DGPs we also compare the small-sample performance of our nonparametric tests to parametric rank tests. Finally, we provide an empirical illustration by testing for income convergence among countries.

Bubble flow in a static magnetic field

A lab-based electrolytic-cell is designed to analyze the effect of external magnetic field on bubble evolution underneath an anode surface. Buckingham Pi theorem is used to provide a complete list of dimensionless parameters for a typical cell configuration. There is an increase in bubble size and the number of bubbles with time. The hydrodynamic convection is apparent due to the effect of electrolyte flow caused by swarm of bubbles rising along the anode surface. The image sequence shows that swarm of bubbles exhibit a swirling flow-field in the presence of the magnetic field. The coalescence process intensifies in an area where magnetic field is higher. As a consequence, bubbles are swept away by the magneto-hydrodynamic (MHD) convection. These results suggest that a magnetic field causes remarkable improvement on the surface coverage of the anode.