相关论文: Sufficient criteria for stabilization properties i…

Inspired by recent developments in the theory of stability results in the context of certain wave type phenomena, we discuss abstract damped hyperbolic type equations given in a block operator matrix form with regards to asymptotic…

We propose and analyze variational source conditions (VSC) for the Tikhonov regularization method with Lp-norm penalties for a general ill-posed operator equation in a Banach space. Our analysis is based on the use of the celebrated…

Conditions for input-output stability of barrier-based model predictive control of linear systems with linear and convex nonlinear (hard or soft) constraints are established through the construction of integral quadratic constraints (IQCs).…

We characterize real Banach spaces $Y$ such that the pair $(\ell_\infty ^n, Y)$ has the Bishop-Phelps-Bollob\'as property for operators. To this purpose it is essential the use of an appropriate basis of the domain space $\R^n$. As a…

It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…

We obtain necessary and sufficient conditions for the existence of strictly stationary solutions of ARMA equations in Banach spaces with independent and identically distributed noise under certain assumptions. First, we obtain conditions…

PI controllers are the most widespread type of controllers and there is an intuitive understanding that if their gains are sufficiently small and of the correct sign, then they always work. In this paper we try to give some rigorous backing…

We present several characterizations, via some weak observability inequalities, on the complete stabilizability for a control system $[A,B]$, i.e., $y'(t)=Ay(t)+Bu(t)$, $t\geq 0$, where $A$ generates a $C_0$-semigroup on a Hilbert space $X$…

In this paper, we study the problem of control of discrete-time linear time varying systems over uncertain channels. The uncertainty in the channels is modeled as a stochastic random variable. We use exponential mean square stability of the…

We study the problem of stabilizing infinite-dimensional systems with input and output quantization. The closed-loop system we consider is subject to packet loss, whose average duration is assumed to be bounded. Given a bound on the initial…

This note presents a sufficient condition for partial approximate ensemble controllability of a set of bilinear conservative quantum systems in an infinite dimensional Hilbert space. The proof relies on classical geometric and averaging…

Various controllability conditions have been obtained by researchers for heterogeneous networked systems with linear dynamics. However, the literature for nonlinear, heterogeneous networked systems is comparatively less. In this paper we…

The distinction between conditional, unconditional, and absolute convergence in infinite-dimensional spaces has fundamental implications for computational algorithms. While these concepts coincide in finite dimensions, the Dvoretzky-Rogers…

A Banach space $\X$ has the complete continuity property (CCP) if each bounded linear operator from $L_1$ into $\X$ is completely continuous (i.e., maps weakly convergent sequences to norm convergent sequences). The main theorem shows that…

Let $L_0$ be a bounded operator on a Banach space, and consider a perturbation $L=L_0+K$, where $K$ is compact. This work is concerned with obtaining bounds on the number of eigenvalues of $L$ in subsets of the complement of the essential…

For a bounded linear operator on a Banach space, we study approximation of the spectrum and pseudospectra in the Hausdorff distance. We give sufficient and necessary conditions in terms of pointwise convergence of appropriate spectral…

In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by…

We introduce the notion of a continuous Schauder frame for a Banach space. This is both a generalization of continuous frames and coherent states for Hilbert spaces and a generalization of unconditional Schauder frames for Banach spaces. As…

In this paper we consider variational regularization methods for inverse problems with large noise that is in general unbounded in the image space of the forward operator. We introduce a Banach space setting that allows to define a…

In this paper we investigate four concepts of exponential stability for difference equations in Banach spaces. Characterizations of these concepts are given. They can be considered as variants for the discrete-time case of the classical…