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This note is devoted to study the output stabilizability of a simplified and a one-dimensional diffusion equation. Necessary and sufficient conditions for the system to be output stabilizable will be given. These conditions are given in…
In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…
In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well-known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the…
The paper is devoted to the study of a stabilization problem for the 2D incompressible Euler system in an infinite strip with boundary controls. We show that for any stationary solution (c, 0) of the Euler system there is a control which is…
It is shown that an internal control based on a moving indicator function is able to stabilize the state of parabolic equations evolving in rectangular domains. For proving the stabilizability result, we start with a control obtained from…
Previously we have proposed that in certain relativistic quantum field theories knotlike configurations may appear as stable solitons. Here we present a detailed investigation of the simplest knotted soliton, the torus-shaped unknot.
We present a direct analytic method towards an estimate for the rate of convergence (to the Euclidean Ball) of Steiner symmetrizations. To this end we present a modified version of a known stability property of the Steiner symmetrization.
Stability is a key property of dynamical systems. In some cases, we want to change unstable system into stable one to achieve certain goals in engineering. Here, we present an example of a $3$ dimensional switched system that alternates…
Considered in this report is the one-dimensional fourth-order dispersive cubic nonlinear Schr\"odinger equation with mixed dispersion. Orbital stability, in the energy space, of a particular standing-wave solution is proved in the context…
This paper deals with global asymptotic stability of prolongations of flows induced by specific vector fields and their prolongations. The method used is based on various estimates of the flows.
Although stable solutions of dynamical systems are typically considered more important than unstable ones, unstable solutions have a critical role in the dynamical integrity of stable solutions. In fact, usually, basins of attraction…
This paper addresses the stabilization issue for fractional order switching systems. Common Lyapunov method is generalized for fractional order systems and frequency domain stability equivalent to this method is proposed to prove the…
In the paper below we consider a problem of stabilization of a priori unknown unstable periodic orbits in non-linear autonomous discrete dynamical systems. We suggest a generalization of a non-linear DFC scheme to improve the rate of…
We give a semi-direct product decomposition of the point stabilisers for the enhanced and exotic nilpotent cones. In particular, we arrive at formulas for the number of points in each orbit over a finite field. This is in accordance with a…
The stability of the Nystr\"om method for the double layer potential equation on simple closed piecewise smooth contours is studied. Necessary and sufficient conditions of the stability of the method are established. It is shown that the…
Immersion and Invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated…
We show that a finite unitary group which has orbits spanning the whole space is necessarily the setwise stabilizer of a certain orbit.
Stability and stabilization of linear port-Hamiltonian systems on infinite-dimensional spaces are investigated. This class is general enough to include models of beams and waves as well as transport and Schr\"odinger equations with boundary…
In this paper we develop further a method for detecting unstable periodic orbits (UPOs) by stabilising transformations, where the strategy is to transform the system of interest in such a way that the orbits become stable. The main…
A stabilized conforming mixed finite element method for the three-field (displacement, fluid flux and pressure) poroelasticity problem is developed and analyzed. We use the lowest possible approximation order, namely piecewise constant…