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Iterative Methods
Published in Jeffery J. Leader, Numerical Analysis and Scientific Computation, 2022
Hence, Jacobi iteration, or any other matrix splitting technique, will converge if the matrix A=U+L+D leads to an M that is a convergent matrix. Since it will converge for any initial guess, stability is immediate (a perturbation of a given xk will necessarily perturb it to another value from which the method converges). The speed of convergence can be shown to be like ρ(M)k, that is, xk−xx0−x=O(ρ(M)k)
A transmission scheme for secure estimation of cyber-physical systems against malicious attack
Published in International Journal of Control, 2023
Lucheng Sun, Li Zhang, Ya Zhang
According to Lemma 3.1, for the estimation system (12) satisfying conditions (17) and (18), holds, where s is any positive integer in . It is obvious that the convergent matrix of increases with the increase of π and when π is larger than certain value, will be divergent. The following lemma from Sinopoli et al. (2004) provides the probability condition of the convergence of in (20).
Region stability and stabilisation of switched linear systems with multiple equilibria
Published in International Journal of Control, 2019
Looking on E − B as a strictly convergent matrix series, one obtains that the two matrix series of ∑+ ∞k = 0Bk and E − B are multipliable. It then follows from Equations (3.9)–(3.13) that which yields that which is the matrix C as defined in Equation (3.14).
Functional observer-based sliding mode control for linear discrete-time-delayed stochastic systems
Published in International Journal of Systems Science, 2018
A diagonal convergent matrix is choose as Consider arbitrarily matrix V as, now, matrix is obtained as