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In contrast to conservative systems, in nonlinear media with gain and loss the dynamics of localized topological structures can exhibit unique features that can be controlled externally. We propose a robust mechanism to perform topological…
We consider both the internal and boundary controllability problems for wave equations under non-negativity constraints on the controls. First, we prove the steady state controllability property with nonnegative controls for a general class…
We characterize the observability property (and, by duality, the controllability and the stabilization) of the wave equation on a Riemannian manifold $\Omega,$ with or without boundary, where the observation (or control) domain is…
The paper considers a stabilizing stochastic control which can be applied to a variety of unstable and even chaotic maps. Compared to previous methods introducing control by noise, we relax assumptions on the class of maps, as well as…
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…
The unavoidable interaction of quantum systems with their environment usually results in the loss of desired quantum resources. Suitably chosen system Hamiltonians, however, can, to some extent, counteract such detrimental decay, giving…
In this paper, we give positive answer to the open question raised in [E. Zuazua, Exponential decay for the semilinear wave equation with localized damping in unbounded domains. J. Math. Pures Appl., 70 (1991) 513--529] on the exponential…
We deduce a sufficient condition of the exponential (integral) turnpike property for infinite dimensional generalized linear-quadratic optimal control problems in terms of structural properties of the control system, such as exponential…
Vibrational structures are susceptible to catastrophic failures or structural damages when external forces induce resonances or repeated unwanted oscillations. One common mitigation strategy is to use dampers to suppress these disturbances.…
This article presents an analysis of the stabilization of a multidimensional partial differential wave equation under a well designed event-triggering mechanism that samples the boundary control input. The wave equation is set in a bounded…
This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…
We investigate global bounded solutions of higher regularity to boundary value problems for a general linear nonautonomous first order 1D hyperbolic system in a strip. We establish the existence of such solutions under the assumption of…
The present paper deals with autonomous integral equations with infinite delay via dynamical system approach. Existence, local exponential attractivity, and other properties of center manifold are established by means of the…
Motivated by networked systems, stochastic control, optimization, and a wide variety of applications, this work is devoted to systems of switching jump diffusions. Treating such nonlinear systems, we focus on stability issues. First…
In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…
In this paper, we will investigate the moment exponential stabilization of highly nonlinear hybrid stochastic differential delay equations. A periodically intermittent controller based on discrete time state observations with asynchronous…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
In this work, we derive a result of exponential stability for a coupled system of partial differential equations (PDEs) which governs a certain fluid-structure interaction. In particular, a three-dimensional Stokes flow interacts across a…
In this paper we consider structurally damped plate and wave equations with point and distributed random forces. In order to treat space dimensions more than one, we work in the setting of $L^q$--spaces with (possibly small) $q\in(1,2)$. We…
Classical discrete-time adaptive controllers provide asymptotic stabilization. While the original adaptive controllers did not handle noise or unmodelled dynamics well, redesigned versions were proven to have some tolerance; however,…