Related papers: Stabilization of Three-Dimensional Collective Moti…
We consider the Navier-Stokes system in a bounded domain with a smooth boundary. Given a sufficiently regular time-dependent global solution, we construct a finite-dimensional feedback control that is supported by a given open set and…
While it is well known that constant rotation induces linear dispersive effects in various fluid models, we study here its effect on long time nonlinear dynamics in the inviscid setting. More precisely, we investigate stability in the 3d…
The phenomenon of linear motion of conductor in a magnetic field is commonly found in electric machineries such as, electromagnetic brakes, linear induction motor, electromagnetic flowmeter etc. The design and analysis of the same requires…
For three-dimensional piecewise-smooth systems of ordinary differential equations, this paper characterises the stability of points that belong to a switching surface and are equilibria of exactly one of the two neighbouring pieces of the…
This paper explores the analytical approach for obtaining the multiple solutions of three-wave interacting system in (1+1) dimensions. We present a novel approach by expressing the wave solutions in terms of Jacobi elliptic functions and…
The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it introduces a precise method to…
This paper considers a group of mobile autonomous agents moving in Euclidean space with point mass dynamics. We introduce a set of coordination control laws that enable the group to generate the desired stable flocking motion. The control…
We describe a situation where an unstable equilibrium in a $3 \times 3$ system of linear differential equations may be stabilized by introducing a delayed response, i.e. converting to a system of delayed differential equations. This…
This paper presents an angle-based approach for distributed formation shape stabilization of multi-agent systems in the plane. We develop an angle rigidity theory to study whether a planar framework can be determined by angles between…
The paper studies the issue of stability of solutions to the Navier-Stokes and damped Euler systems in periodic boxes. We show that under action of fast oscillating-in- time external forces all two dimensional regular solutions converge to…
Dimensional regularization is used to derive the equations of motion of two point masses in harmonic coordinates. At the third post-Newtonian (3PN) approximation, it is found that the dimensionally regularized equations of motion contain a…
We study stability patterns in the high dimensional rational homology of unordered configuration spaces of manifolds. Our results follow from a general approach to stability phenomena in the homology of Lie algebras, which may be of…
This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling…
We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum methods.…
This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…
The thermodynamic equilibrium conditions for compact structures composed by mass varying particles are discussed assuming that the so-called dynamical mass behaves like an additional extensive thermodynamic degree of freedom. It then…
We study the shape stability of disks moving in an external Laplacian field in two dimensions. The problem is motivated by the motion of ionization fronts in streamer-type electric breakdown. It is mathematically equivalent to the motion of…
The task of inducing, via continuous static state-feedback control, an asymptotically stable heteroclinic orbit in a nonlinear control system is considered in this paper. The main motivation comes from the problem of ensuring convergence to…
It is shown that, under suitable conditions, involving in particular the existence of analytic constants of motion, the presence of Lie point symmetries can ensure the convergence of the transformation taking a vector field (or dynamical…
This paper presents a combined sliding-mode control and subspace stabilization methodology for orbital stabilization of periodic trajectories in underactuated mechanical systems with one degree of underactuation. The approach starts with…