Abstract: In this paper, reliable consensus of multi-agent systems
with sampled-data is investigated. By using a suitable
Lyapunov-Krasovskii functional and some techniques such as
Wirtinger Inequality, Schur Complement and Kronecker Product, the
results of such system are obtained by solving a set of Linear Matrix
Inequalities (LMIs). One numerical example is included to show the
effectiveness of the proposed criteria.
Abstract: The generalized Higham matrix is a complex symmetric matrix A = B + iC, where both B ∈ Cn×n and C ∈ Cn×n are Hermitian positive definite, and i = √−1 is the imaginary unit. The growth factor in Gaussian elimination is less than 3√2 for this kind of matrices. In this paper, we give a new brief proof on this result by different techniques, which can be understood very easily, and obtain some new findings.
Abstract: In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.