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The paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.

Röhmel's equation for quadratic forms.

T.M.K. Davison (1987)

Aequationes mathematicae

Rotation du sous-espace invariant d’un endomorphisme symétrique de $𝐑^{n}$ par une perturbation symétrique

B. Escofier, B. Le Roux (1975)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Rotation numbers for Jacobi matrices with matrix entries.

Schulz-Baldes, Hermann (2007)

Mathematical Physics Electronic Journal [electronic only]

Round Quadratic Forms.

Murray Marshall (1974)

Mathematische Zeitschrift

Row Hadamard majorization on $𝐌_{m, n}$

Abbas Askarizadeh, Ali Armandnejad (2021)

Czechoslovak Mathematical Journal

An $m \times n$ matrix $R$ with nonnegative entries is called row stochastic if the sum of entries on every row of $R$ is 1. Let $𝐌_{m, n}$ be the set of all $m \times n$ real matrices. For $A, B \in 𝐌_{m, n}$ , we say that $A$ is row Hadamard majorized by $B$ (denoted by $A ≺_{R H} B)$ if there exists an $m \times n$ row stochastic matrix $R$ such that $A = R \circ B$ , where $X \circ Y$ is the Hadamard product (entrywise product) of matrices $X, Y \in 𝐌_{m, n}$ . In this paper, we consider the concept of row Hadamard majorization as a relation on $𝐌_{m, n}$ and characterize the structure of all linear operators $T : 𝐌_{m, n} \to 𝐌_{m, n}$ preserving (or...

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