this paper is concerned with the problem of synchronization for complex dynamic networks with state and coupling time-delays. therefore, larger class and more complicated complex dynamic networks can be considered for the synchronization problem. based on the lyapunov-krasovskii functional, a delay-independent criterion is obtained and formulated in the form of linear matrix inequalities (lmis)...

Let M be a finite monoid of Lie type (these are the finite analogues of linear algebraic monoids) with group of units G . The multiplicative semigroup ^AfF), where F is a finite field, is a particular example. Using HarishChandra's theory of cuspidal representations of finite groups of Lie type, we show that every complex representation of M is completely reducible. Using this we characterize t...

The paper contains some new results and a review of recent achievements, concerning the multisupport solutions to matrix models. In the leading order of the ’t Hooft expansion for matrix integral, these solutions are described by quasiclassical or generalized Whitham hierarchies and are directly related to the superpotentials of four-dimensional N = 1 SUSY gauge theories. We study the derivativ...

In this paper, we present the notion of complex interval matrix. Further, discuss algebraic structure set all $(m\times n)$ matrices by using tools quasilinear functional analysis. Finally, put a norm on space and calculate matrices.