In the vector-field guided path-following problem, a sufficiently smooth vector field is designed such that its integral curves converge to and move along one-dimensional geometric desired path. The existence of singular points where vanishes creates topological obstruction global convergence path some associated analysis has been conducted in [1]. this paper, we strengthen result [1, Theorem 2...

We calculate the four-loop β-function for the generalised Wess-Zumino model. We use the result and Padé-Borel summation to discuss the domain of attraction of the quasi-infra-red fixed point of the top-quark Yukawa coupling in the supersymmetric standard model, and argue that the domain is in fact substantial.

We prove that the problem of counting the number of stable states in a given Hopfield net is #P-complete and the problem of computing the size of the attraction domain of a given stable state is NP-hard.

This work presents an approach for estimating the domain of attraction for polynomial systems with state and control-signal constraints including saturation. In many problems, it is possible to derive global stability properties for such systems, neglecting constraints. Consideration of the constraints usually makes the problem much more involved. In this paper, the stability analysis performed...

This paper generalizes our recent results on the null controllable regions and the stabilizability of exponentially unstable linear systems subject to symmetric actuator saturation. The description of the null controllable region carries smoothly from the symmetric case to the asymmetric case. As to stabilization, we have to take a quite di erent approach since the development of our earlier re...

Takagi–Sugeno (TS) fuzzy models can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear inputoutput submodels. In this paper, the TS fuzzy modeling approach is utilized to carry out the stability analysis and control design for nonlinear systems with actuator saturation. The TS fuzzy representation of a nonlinear...

An alternative method to formulate the stable Model Predictive Control (MPC) optimization problem, which allows controlling unstable systems with a large domain of attraction, is presented in this work. Usually, stability is guaranteed by means of an appropriate selection of a terminal cost, a terminal constraint, and a local unconstrained controller for predictions beyond the control horizon. ...

We study the first exit times form a reduced domain of attraction of a stable fixed of the Chafee-Infante equation when perturbed by a heavy tailed Lévy noise with small intensity.

We study functional limit theorems for linear type processes with short memory under the assumption that the innovations are dependent identically distributed random variables with infinite variance and in the domain of attraction of stable laws.