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Fundamentals of Circuit Networks
Published in Kaixue Ma, Kiat Seng Yeo, Low-Power Wireless Communication Circuits and Systems, 2018
Wei Xu, Kaixue Ma, Kiat Seng Yeo
or the Z matrix of the combined Z matrix is [Z]=[Za]+[Zb]. $$ [Z] = [Z_{a} ] + [Z_{b} ] . $$
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Published in S.P. Bhattacharyya, L.H. Keel, of UNCERTAIN DYNAMIC SYSTEMS, 2020
Dennis S. Bernstein, David C. Hyland
Henceforth we consider the case in which A is nonsingular, that is, in which —A is a nonsingular M-matrix. Numerous necessary and sufficient conditions for a Z-matrix to be a nonsingular M-matrix are given by Theorem 6.2.3 of [6]. The following easily verified condition is sufficient but not necessary.
Upper solution bound of the CCARE and its application in multi-agent systems with time-delay in the state
Published in International Journal of Control, 2023
Throughout this paper, let be the set of real (complex) matrices. For , the notation is used to denote that A is a symmetric positive definite (semi-definite) matrix. Inequality means matrix is positive (semi)definite. For , let be the non-increasing order eigenvalues of A, and . We assume to be the transpose and the inverse of A, respectively. A is called a Z-matrix if all its off-diagonal elements are nonpositive. It is obvious that any Z-matrix A can be written as sI−B with B is nonnegative. A Z-matrix A is called an M-matrix if . For two vectors and , is equivalent to . Symbol represents the matrix measure of A and is defined as .
Analysis on structured stability of highly nonlinear pantograph stochastic differential equations
Published in Systems Science & Control Engineering, 2019
Mingxuan Shen, Chunhui Mei, Shounian Deng
Let be a Z-matrix. Then A is a nonsingular M-matrix if and only if one of the the following statements holds: exists and its elements are all nonnegative.There exists x>0 in such that Ax>0.
Stochastic Nicholson-type delay differential system
Published in International Journal of Control, 2021
A real matrix is said to be a Z-matrix if , . Moreover, if it is a Z-matrix and , , then the matrix A is said to be a L-matrix.