in this paper, a new method is derived for the existence of a common quadratic Lyapunov function for Robust Stability Analysis of Fuzzy Elman Neural Network using joint spectral radius spectral radius of Matrix.

Abstract. The joint spectral radius is the extension to two or more matrices of the (ordinary) spectral radius ρ(A) = max |λi(A)| = lim‖A m‖1/m. The extension allows matrix products Πm taken in all orders, so that norms and eigenvalues are difficult to estimate. We show that the limiting process does yield a continuous function of the original matrices—this is their joint spectral radius. Then ...

The decrease of the spectral radius, an important characterizer of network dynamics, by removing links is investigated. The minimization of the spectral radius by removing m links is shown to be an NP-complete problem, which suggests considering heuristic strategies. Several greedy strategies are compared, and several bounds on the decrease of the spectral radius are derived. The strategy that ...

The problem of the title is to construct an analytic k × k matrixvalued function in the unit disc with a number of prescribed derivatives at 0 and with spectral radius bounded by 1. We show that the problem can be reduced to an interpolation problem for the symmetrized polydisc Gk, and thereby show that, in the case of derivatives of orders 0 and 1 being prescribed, the problem is equivalent to...

The odd wheel W2k+1 is the graph formed by joining a vertex to cycle of length 2k. In this paper, we investigate largest value spectral radius adjacency matrix an n-vertex that does not contain W2k+1. We determine structure extremal graphs for all k?2,k??{4,5}. When k=2, show these are among Turán-extremal on n vertices do and have maximum number edges, but when k?9, family disjoint.

The author of this dissertation studies the spectral properties of high-contrast photonic crystals, i.e. periodic electromagnetic waveguides made of two materials (a connected phase and included phase) whose electromagnetic material properties are in large contrast. A spectral analysis of 2nd-order divergence-form partial differential operators (with a coupling constant k) is provided. A result...

We use induction and interpolation techniques to prove that a composition operator induced by a map φ is bounded on the weighted Bergman space Aα(H) of the right half-plane if and only if φ fixes ∞ non-tangentially, and has a finite angular derivative λ there. We further prove that in this case the norm, essential norm, and spectral radius of the operator are all equal, and given by λ.

The spectral radius p(A) of the adjacency matrix A of a graph G with e edges satisfiesp(A)<i(-l+~~).Equalityoccnrsifandonlyif e= i andGisa disjoint union of the complete graph K, and isolated vertices. 0 Let A be a symmetric (0,l) matrix with zero trace (i.e., the adjacency matrix of a graph G). Let the number of l’s of A be 2 (k) (so G has (i) edges). R. A. Brualdi and A. J. Hoffmann [l, Theor...