A simple, necessary, and sufficient condition ensuring that a real matrix of dimension three is similar to Metzler exhibited. When this satisfied, construction the transfer given. This used design an interval observer for family continuous-time systems. An example provided with so-called love dynamics in case limit cycles

A translation surface on (S,Σ) gives rise to two transverse measured foliations F ,G on S with singularities in Σ, and by integration, to a pair of cohomology classes [F ], [G] ∈ H(S,Σ;R). Given a measured foliation F , we characterize the set of cohomology classes b for which there is a measured foliation G as above with b = [G]. This extends previous results of Thurston [Th] and Sullivan [Su]...

Described is a not-a-priori-exponential algorithm which for each n×n interval matrix A and for each interval n-vector b in a finite number of steps either computes the interval hull of the solution set of the system of interval linear equations Ax = b, or finds a singular matrix S ∈ A.

The necessary and sufficient condition for stability of K-symmetrizable interval matrix is given. An algorithm for checking stability of K-symmetrizable interval matrix is proposed.

The decision making problem with interval numbers is an important topic of uncertain multiple attribute decision making. A difficulty to solve the interval decision making problems is the ranking method of interval numbers, because among the interval numbers exist cross, it’s difficult to ranking the alternatives directly. This paper studied how to make use of the traditional method for certain...

In this paper, the notions of (T, S)-composition matrix and (T, S)interval-valued intuitionistic fuzzy equivalence matrix are introduced where (T, S) is a dual pair of triangular module. They are the generalization of composition matrix and interval-valued intuitionistic fuzzy equivalence matrix. Furthermore, their properties and characterizations are presented. Then a new method based on α̃−mat...

Max-plus algebra is the algebraic structure in which classical addition and multiplication are replaced by a⊕b = max{a, b} and a⊗b = a+b, respectively. Each system of linear equation in max-plus algebra we can write in the matrix form A⊗ x = b, where A and b are matrix and vector of suitable size. If we replace the matrix elements with matrix interval A = [A,A] and vector elements by vector int...

This paper examines the relationship between the dynamics of large networks and of their smaller factor-networks (factors) obtained through the factorization of the network's graph representation. We speci cally examine dynamics of networks which have Z-matrix state matrices. We perform a Cartesian product decomposition on its network structure producing factors which also have Z-matrix dynamic...