Stabilization of two-dimensional single-input bilinear systems with a finite number of constant feedback controllers

2002 ◽  
Author(s):  
Bo Hu ◽  
Guisheng Zhai ◽  
A.N. Michel
Keyword(s):  
Finite Number ◽  
Bilinear Systems ◽  
Two Dimensional ◽  
Feedback Controllers ◽  
Single Input

scholarly journals Gap opening in two-dimensional periodic systems

2019 ◽  
Vol 23 (01) ◽  
pp. 1950080
Author(s):  
D. I. Borisov ◽  
P. Exner
Keyword(s):  
Differential Operator ◽  
Finite Number ◽  
Distinctive Feature ◽  
Perturbation Parameter ◽  
Periodic Systems ◽  
Order Differential Operator ◽  
Two Dimensional ◽  
Gap Opening ◽  
Gap Control ◽  
Waveguide System

We present a new method of gap control in two-dimensional periodic systems with the perturbation consisting of a second-order differential operator and a family of narrow potential “walls” separating the period cells in one direction. We show that under appropriate assumptions one can open gaps around points determined by dispersion curves of the associated “waveguide” system, in general any finite number of them, and to control their widths in terms of the perturbation parameter. Moreover, a distinctive feature of those gaps is that their edge values are attained by the corresponding band functions at internal points of the Brillouin zone.

On the existence and ‘blow-up’ of solutions to a two-dimensional nonlinear boundary-value problem arising in corrosion modelling

2003 ◽  
Vol 133 (1) ◽  
pp. 119-149 ◽  
Author(s):  
Otared Kavian ◽  
Michael Vogelius
Keyword(s):  
Variational Principle ◽  
Boundary Value Problem ◽  
Finite Number ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Boundary Value ◽  
Classical Solutions ◽  
Two Dimensional ◽  
Limiting Behaviour ◽  
Corrosion Modelling

Let Ω be a bounded C2,α domain in R2. We prove that the boundary-value problem Δυ = 0 in Ω, ∂υ/∂n = λsinh(υ) on ∂Ω, has infinitely many (classical) solutions for any given λ > 0. These solutions are constructed by means of a variational principle. We also investigate the limiting behaviour as λ → 0+; indeed, we prove that each of our solutions, as λ → 0+, after passing to a subsequence, develops a finite number of singularities located on ∂Ω.

On the stability of steady-states of a two-dimensional system of ferromagnetic nanowires

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Sharad Dwivedi ◽  
Shruti Dubey
Keyword(s):  
Finite Number ◽  
Steady States ◽  
Dimensional System ◽  
Two Dimensional ◽  
Ferromagnetic Nanowires ◽  
Two Dimensional System ◽  
The Stability

AbstractWe investigate the stability features of steady-states of a two-dimensional system of ferromagnetic nanowires. We constitute a system with the finite number of nanowires arranged on the

The Measure of Plane Sets

1943 ◽  
Vol 39 (1) ◽  
pp. 51-53
Author(s):  
P. A. P. Moran
Keyword(s):  
Finite Number ◽  
Coordinate System ◽  
Lebesgue Measure ◽  
Upper Bound ◽  
Two Dimensional ◽  
Image Position ◽  
Bounded Sets ◽  
Dimensional Lebesgue Measure

We consider bounded sets in a plane. If X is such a set, we denote by Pθ(X) the projection of X on the line y = x tan θ, where x and y belong to some fixed coordinate system. By f(θ, X) we denote the measure of Pθ(X), taking this, in general, as an outer Lebesgue measure. The least upper bound of f (θ, X) for all θ we denote by M. We write sm X for the outer two-dimensional Lebesgue measure of X. Then G. Szekeres(1) has proved that if X consists of a finite number of continua,Béla v. Sz. Nagy(2) has obtained a stronger inequality, and it is the purpose of this paper to show that these results hold for more general classes of sets.

Structural control of single-input rank one bilinear systems

Automatica ◽  
2016 ◽  
Vol 64 ◽  
pp. 8-17 ◽  
Author(s):  
Supratim Ghosh ◽  
Justin Ruths
Keyword(s):  
Structural Control ◽  
Bilinear Systems ◽  
Rank One ◽  
Single Input

A two-dimensional problem for an anisotropic body with a finite number of “tunnel” cracks

1995 ◽  
Vol 76 (3) ◽  
pp. 2358-2363
Author(s):  
S. A. Kaloerov ◽  
N. M. Neskorodev ◽  
L. I. Krasnokutskaya
Keyword(s):  
Finite Number ◽  
Anisotropic Body ◽  
Two Dimensional ◽  
Dimensional Problem
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