Related papers: Computing the nearest $\Omega$-admissible descript…

In this paper, we provide a dissipative Hamiltonian (DH) characterization for the set of matrices whose eigenvalues belong to a given LMI region. This characterization is a generalization of that of Choudhary et al. (Numer. Linear Algebra…

In this paper, we study the nearest stable matrix pair problem: given a square matrix pair $(E,A)$, minimize the Frobenius norm of $(\Delta_E,\Delta_A)$ such that $(E+\Delta_E,A+\Delta_A)$ is a stable matrix pair. We propose a reformulation…

In this paper, we find necessary and sufficient conditions to identify pairs of matrices $X$ and $Y$ for which there exists $\Delta \in \mathbb C^{n,n}$ such that $\Delta+\Delta^*$ is positive semidefinite and $\Delta X=Y$. Such a $\Delta$…

In this paper, we consider the problem of approximating a given matrix with a matrix whose eigenvalues lie in some specific region \Omega, within the complex plane. More precisely, we consider three types of regions and their intersections:…

In these lectures notes, we review our recent works addressing various problems of finding the nearest stable system to an unstable one. After the introduction, we provide some preliminary background, namely, defining Port-Hamiltonian…

Given a self-adjoint matrix $A$ and an index $h$ such that $\lambda_h(A)$ lies in a cluster of eigenvalues of $A$, we introduce the novel class of $\Lambda$-admissible subspaces of $A$ of dimension $h$. First, we show that the low-rank…

Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…

We consider the singular optimal control problem of minimizing the energy supply of linear dissipative port-Hamiltonian descriptor systems subject to control and terminal state constraints. To this end, after reducing the problem to an ODE…

We address Calder\'on's problem of stably determining the anisotropic complex admittivity $\sigma$ in a domain $\Omega\subset\mathbb{R}^n$, with $n\geq3$, representing a conducting medium, in terms of a Dirichlet-to-Neumann map locally…

We study the characterization of several distance problems for linear differential-algebraic systems with dissipative Hamiltonian structure. Since all models are only approximations of reality and data are always inaccurate, it is an…

Let $\Omega \subset \mathbb{R}^n$ be a bounded smooth domain (open and connected) in $\mathbb{R}^n$. Given $u_0\in L^2(\Omega)$, $g\in L^\infty(\Omega)$ and $\lambda \in \mathbb{R}$, our purpose is to describe the asymptotic behavior of…

This paper considers feedback methods for ensemble reachability of parameter-dependent linear systems $(A(\theta),B(\theta))$, where the parameter $\theta$ is varying over a compact Jordan arc in the complex plane. Recently, pointwise…

Let $G = (V, E)$ be a graph. We define matrices $M(G; \alpha, \beta)$as $\alpha D + \beta A$, where $\alpha$, $\beta$ are real numbers such that $(\alpha, \beta) \neq (0, 0)$ and $D$ and $A$ are the diagonal matrix and adjacency matrix of…

Given a matrix $A\in \R^{n\times n}$ and a tall rectangular matrix $B \in \R^{n\times q}$, $q < n$, we consider the problem of making the pair $(A,B)$ dissipative, that is the determination of a {\it feedback} matrix $K \in \R^{q\times n}$…

Let g be a complex simple Lie algebra and e a nilpotent element of g. We are interested in the isomorphism question (raised by Premet) between the finite W-algebras constructed from some nilpotent subalgebras of g called e-admissible. We…

Topologies $\tau, \sigma$ on a set $X$ are called $\pi$-compatible if $\tau$ is a $\pi$-network for $\sigma$, and vice versa. If topologies $\tau, \sigma$ on a set $X$ are $\pi$-compatible then the families of nowhere dense sets (resp.…

We study a pair (\mathcal{S}_0,\mathcal{S}) of irreducible Hermitian Symmetric Spaces of compact type (cHSS) in this paper, with the first aim being classifying all the admissible pairs (\mathcal{S}_0,\mathcal{S})). This notion is a natural…

An elementary set of non-Hermitian $N$ by $N$ matrices $H^{(N)}(\lambda) \neq [ H^{(N)}(\lambda)]^\dagger$ with real spectra is considered, assuming that each of these matrices represents a selfadjoint quantum Hamiltonian in an {\it ad hoc}…

In this paper, we consider the problem of computing the nearest stable matrix to an unstable one. We propose new algorithms to solve this problem based on a reformulation using linear dissipative Hamiltonian systems: we show that a matrix…

In this paper we consider the functional \begin{equation*} E_{p,\la}(\Omega):=\int_\Omega \dist^p(x,\pd \Omega )\d x+\la \frac{\H^1(\pd \Omega)}{\H^2(\Omega)}. \end{equation*} Here $p\geq 1$, $\la>0$ are given parameters, the unknown…