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Nonnegative Stabilization of Interval Discrete Systems
Published in S.P. Bhattacharyya, L.H. Keel, of UNCERTAIN DYNAMIC SYSTEMS, 2020
As we have pointed out before the class of M-matrices, although they are not nonnegative, are closely related to nonnegative matrices with remarkable properties. The main diagonal entries of an M-matrix are nonnegative and all its other entries are nonpositive. Furthermore the principal minors and the inverse of an M-matrix are nonnegative. Since all the eigenvalues of an M-matrix have nonnegative real parts, the nagative of an M-matrix becomes a stable Metzler matrix which establishes a direct link to the stability of continuous time systems.
Actuator fault detection for uncertain systems based on the combination of the interval observer and asymptotical reduced-order observer
Published in International Journal of Control, 2020
Xiangming Zhang, Fanglai Zhu, Shenghui Guo
For continuous-time dynamic linear system , if is a Metzler matrix and , then for any initial state satisfying , the state solution of the system will satisfy .
Non-fragile reliable control for positive Markovian jump systems based on event-triggered mechanism
Published in Journal of Control and Decision, 2021
Yinggang Feng, Junfeng Zhang, Shuo Li, Shizhou Fu
Notation : Let (or, ), (or, ), and be the sets of real numbers, n-dimensional vectors (or, non-negative vectors) and matrices, respectively. and denote the sets of non-negative and positive integers, respectively. The symbol refers to mathematical expectation. is a diagonal matrix consisting of diagonal elements . A matrix A is said to be a Metzler matrix if its off-diagonal elements are all non-negative. represents the convex hull. For a matrix , () means that . () means that . Similarly, means that . The transpose of matrix A is . A matrix I denotes the identity matrix with an appropriate dimension. Define and , and as a matrix whose elements are all 1. The 1-norm and Euclidean norm of a vector are defined as and , respectively, where is the kth element of x.