The Global Convergence of the Nonlinear Power Method for Mixed-Subordinate Matrix Norms

We analyze the global convergence of the power iterates for the computation of a general mixed-subordinate matrix norm. We prove a new global convergence theorem for a class of entrywise nonnegative matrices that generalizes and improves a well-known results for mixed-subordinate $$\ell ^p$$ ℓ p matrix norms. In particular, exploiting the Birkoff–Hopf contraction ratio of nonnegative matrices, we obtain novel and explicit global convergence guarantees for a range of matrix norms whose computation has been recently proven to be NP-hard in the general case, including the case of mixed-subordinate norms induced by the vector norms made by the sum of different $$\ell ^p$$ ℓ p -norms of subsets of entries.

Generalized solution to the problem of reconstructing the graph structure based on the transfer function matr ix

This study presents a generalized solution to the problem of restoring the structure of a graph based on the method of minimizing the transfer matrix norm, consistent with the Euclidean vector norms, with a minimum and extended set of constraints. The problem of complete reconstruction of the adjacency matrix, in the presence of pairs of vectors of exogenous and endogenous influences, expressing the intrinsic resonance properties of the network, and positive semidefinite constraints on the matrix of variables, is a generalization of the problem of reconstructing the structure of a graph from the eigenvalues of the Laplace matrix.

Simple Algebraic Criteria for Asymptotic Stability of a Class of TS Fuzzy Time-Delay Switched Systems

This paper investigates the asymptotic stability of a class of TS fuzzy switched systems when an arbitrary switching strategy is adopted. The proposed method, applied to neutral and retarded-type systems, is based on the vector-norms approach. The idea consists in defining a common comparison system to all the fuzzy models. If this comparison system can be described by a state matrix that fulfills the properties of the opposite of an M-matrix, then we can conclude on the asymptotic stability of the initial system via simple algebraic delay-independent conditions.