It dealt with the controller design problem for switched neutral systems with two classes of uncertainties and time-varying delay in a range. Based on the average dwell time method, by choosing a piecewise Lyapunov-Krasovskii functional, delay-range-dependent corresponding sufficient conditions of the feedback delayed controllers were derived in terms of linear matrix inequalities. Moreover, much less conservative results was obtained. The effectiveness of the proposed robust control scheme was demonstrated by simulation examples.

Let A=(a _ij)∈C ^{n ×n}, if there existsα∈(0,1) [WTBZ]which can make |a _ii|≥R ^α _iS ^{1- α} _i be right for i∈N={1,2,…,n},then  is called anα-chain diagonally dominant matrix.It gave an equivalent condition for chain strictly diagonally dominant matrices，and obtains a necessary condition for a matrix to be a nonsingular H-matrix indirectly. The result obtained improves the known corresponding results．At last, some numerical examples are given for illustrating advantages of the result.

The local discontinuous Galerkin (LDG) method using to solve poisson equations on two-dimensional domain was introduced. The construction of LDG was described. The algorithm formulation and practical implementation with linear elements and quadratic elements were discussed in triangular element cases, including numerical quadrature rules, mass matrix formula and iterative methods to solve system. At last, numerical experiments were presented to verify the accuracy of convergence.

 

 

Some iteration methods for solving linear system were studied，when coefficient matrix is α-diagonal strictly dominance or doubly diagonal strictly dominance, and some convergence theorems were given. Results obtained were applicable to α-diagonal strictly dominance matrix or doubly diagonal strictly dominance matrix, and improved the known results and were suited to extended matrices. Finally, an numerical examples were given for illustrating advantage of results．

Let [WTHX]A[WTBZ]=([WTBX]aij)∈Cn×n, if there exists α∈(0,1) which can make |aii|≥Rαi(A)S1-αi(A)  be right for i∈N={1,2,…,n}, then [WTHX]A[WTBZ] is called an Ostrowski diagonally dominant matrix. We extended the concept to generalized Ostrowski diagonally dominant matrix，and obtained a new criteria conditions for a matrix to be a nonsingular [WTHX]H[WTBZ]-matrix. The theory of Ostrowski diagonally dominant matrix and nonsingular [WTHX]H[WTBZ]-matrix was improved and completed. These conclusions provide strong basis for the research of relative fields, such as computational mathematics, matrix theory, control theory, mathematical economics, etc.

Let G be a simple graph with n vertices, the new upper bound on the sum of the Q spectral radius of a graph and its complement were given by its m edges, minimal degree of a vertex δ, maximal degree of a vertex Δ and chromatic number k． When graph G has no isolated vertex ,we have 2(n-1)≤ρ(Q(G))+ρ(Q([AKG-]))≤2(Δ-δ+n-1) and ρ(Q(G))+ρQ([AKG-]))≤2n-3+[KF(][JB((]2-[SX(]1[]2[SX)][JB))](n-1)n[KF)]，where t=min{k,[AKk-]}. When graph [AKG-] has l isolated vertices ,we have ρ(Q(G))+ρ(Q([AKG-]))≤2n-3+[KF(][JB((]2-[SX(]1[]k[SX)][JB))](n-1)2+l[KF)]. At the same time the upper bound on the sum of the Laplace spectral radius of a graph and its complement was given.

According to several iteration methods for solving large linear system, when coefficient matrix is of α-diagonal strictly dominance, a new upper bound for the spectral radius of the iterative matrices was presented. Parameter estimation for JOR method was discussed. Results are applicable not only for α-diagonal strictly dominance, but also for generalized α-diagonal strictly dominant matrices. The known conclusion was improved. Finally, two numerical examples were given for illustrating advantage of results.

For the linear equations system whose coefficient matrix is of -diagonal strictly dominance or doubly -chain diagonal strictly dominance, convergence properties of some iteration methods were studied and some convergence theorems were given, which solves the problem of spectral radius of iterative matrices. Results are applicable not only for -diagonal strictly dominance matrix or doubly diagonal strictly dominance matrices, but also for generalized strictly diagonally dominant matrices. Finally, numerical examples were given for illustrating advantage of results.

Let G be a simple graph with n vertices and ρ(G) be its spectral radius．Let [AKG-] be the complement [KG*3]graph [KG*3]of [KG*3]G, [KG*3]and ρ([AKG-]) be the spectral radius of [AKG-]．The upper bound on sum of the spectral radius of G and [AKG-] were given, and the upper bound on sum of the spectral radius of G and [AKG-] were given when G be unconnected and [AKG-] be connected .

Let [WTHX]A[WTBX]=(aij)∈Cn×n, [WTBZ]if there exists[WTBX] α[WTBZ]∈（0，1）, which can make[WTBX] |aiiajj|≥（RiRj）α（SiSj）1-α[WTBZ] be right for[WTBX] i≠j（i，j∈N={1，2，…，n}）, [WTBZ]then [WTHX]A[WTBZ] is called an α-doubly diagonally dominant matrix. First it is extended the concept to generalized α-doubly diagonally dominant matrix, and obtained a new necessary and sufficient condition for [WTHX]A[WTBZ] to be generalized α-doubly diagonally dominant matrices, improving and generalizing the related results. This result enriches and improves the theory of α-doubly diagonally dominant matrices.