We prove a converse Lyapunov theorem for almost sure stabilizability of controlled diffusions: given a stochastic system a.s. open loop stabilizable at the origin, we construct a lower semicontinuous positive definite function whose level sets form a local basis of viable neighborhoods of the equilibrium. This result provides, with the direct Lyapunov theorem proved in a companion paper, a comp...

In this paper, a new fuzzy logic controller—fuzzy logic constant controller (FLCC) is introduced to chaotic signals controlling. The main ideas of the FLCC are described as follows: (1) proving the two chaotic systems are going to achieve asymptotically stable via Lyapunov direct method; (2) via detecting the sign of the errors, the appropriate fuzzy logic control scheme is operated; (3) choosi...

We derive explicit stability conditions for time-dependent difference equations with several delays in C n (the set of n complex vectors) and estimates for the size of the solutions. The growth rates obtained here are not necessarily decay rates. 1. Introduction. Stability of systems of difference equations with delays has been discussed by many authors, for example, see Gil' and Cheng [6], Zha...

This study employed Lyapunov function method to investigate the stability of nonlinear ordinary differential equations. Using direct method, we constructed sixth order We find $ V(x) $, a quadratic form, positive definite and U(x) which is also was chosen such that derivative with respect time equal negative value $.

Characterization of the stability boundary of differential-algebraic (DAE) systems is more complicated than for systems described by ordinary differential equations (ODEs). In addition to unstable equilibria and periodic orbits, algebraic singularity plays an important role in defining the stability boundary. This paper presents a Lyapunov-based method for direct assessment of transient singula...

Lyapunov functions are an important tool to determine the basin of attraction of exponentially stable equilibria in dynamical systems. In Marinosson (2002), a method to construct Lyapunov functions was presented, using finite differences on finite elements and thus transforming the construction problem into a linear programming problem. In Hafstein (2004), it was shown that this method always s...

A qualitative method is explored for analyzing the stability of systems. The approach is a generalization of the celebrated Lyapunov method. Whereas classically, the Lyapunov method is based on the simple comparison theorem, deriving suitable candidate Lyapunov functions remains mostly an art. As a result, in the realm of delay equations, such Lyapunov methods can be quite conservative. The gen...

In this paper we propose a controller architecture for High Voltage Direct Current (HVDC) based on our adaptive network called Fuzzified Input Perceptron (FIP). In FIP, the THEN part membership function and defuzzification steps are combined together, as a result the overall structure becomes simple. Moreover the initial setting of FIP’s parameters can be selected based on expert knowledge. FIP...

This paper presents the trajectory tracking control of an autonomous underwater vehicle (AUV). To cope with parametric uncertainties owing to the hydrodynamic effect, an adaptive control law is developed for the AUV to track the desired trajectory. This desired state-dependent regressor matrix-based controller provides consistent results under hydrodynamic parametric uncertainties. Stability of...

Clustering in ensembles of globally coupled identical chaotic oscillators is reconsidered using a twofold approach. Stability of clusters towards "emanation" of the elements is described with the evaporation Lyapunov exponents. It appears that direct numerical simulations of ensembles often lead to spurious clusters that have positive evaporation exponents, due to a numerical trap. We propose a...