共查询到20条相似文献，搜索用时 15 毫秒
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Xiongping Dai Tingwen Huang Yu Huang Yi Luo Gang Wang Mingqing Xiao 《Journal of The Franklin Institute》2017,354(10):4126-4155
Given any finite family of real d-by-d nonsingular matrices by extending the well-known Li–Yorke chaos of a deterministic nonlinear dynamical system to a discrete-time linear inclusion or hybrid or switched system:
we study the chaotic dynamics of the state trajectory (xn(x0, σ))n ≥ 1 with initial state governed by a switching law . Two sufficient conditions are given so that for a “large” set of switching laws σ, there exhibits the scrambled dynamics as follows: for all This implies that there coexist positive, zero and negative Lyapunov exponents and that the trajectories (xn(x0, σ))n ≥ 1 are extremely sensitive to the initial states . We also show that a periodically stable linear inclusion system, which may be product unbounded, does not exhibit any such chaotic behavior. An explicit simple example shows the discontinuity of Lyapunov exponents with respect to the switching laws. 相似文献
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Xingping Sheng 《Journal of The Franklin Institute》2018,355(10):4282-4297
The present work proposes a relaxed gradient based iterative (RGI) algorithm to find the solutions of coupled Sylvester matrix equations . It is proved that the proposed iterative method can obtain the solutions of the coupled Sylvester matrix equations for any initial matrices X0 and Y0. Next the RGI algorithm is extended to the generalized coupled Sylvester matrix equations of the form . Then, we compare their convergence rate and find RGI is faster than GI, which has maximum convergence rate, under an appropriative positive number ω and the same convergence factor µ1 and µ2. Finally, a numerical example is included to demonstrate that the introduced iterative algorithm is more efficient than the gradient based iterative (GI) algorithm of (Ding and Chen 2006) in speed, elapsed time and iterative steps. 相似文献
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Akbar Zada Bakht Zada Jinde Cao Tongxing Li 《Journal of The Franklin Institute》2017,354(14):6247-6257
Let {Πτ(m, n): m?≥?n?≥?0} be the family of periodic discrete transition matrices generated by bounded valued square matrices Λτ(n), where is an arbitrary switching signal. We prove that the family {Πτ(m, n): m?≥?n?≥?0} of bounded linear operator is uniformly exponentially stable if and only if the sequence is bounded. 相似文献
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This paper studies the stability of linear continuous-time systems with time-varying delay by employing new Lyapunov–Krasovskii functionals. Based on the new Lyapunov–Krasovskii functionals, more relaxed stability criteria are obtained. Firstly, in order to coordinate with the use of the third-order Bessel-Legendre inequality, a proper quadratic functional is constructed. Secondly, two couples of integral terms and are involved in the integral functionals and respectively, so that the coupling information between them can be fully utilized. Finally, two commonly-used numerical examples are given to demonstrate the effectiveness of the proposed method. 相似文献
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Michael Gil’ 《Journal of The Franklin Institute》2018,355(10):4241-4247
We consider the function Lyapunov equation where A and C are given matrices, f(z) is a function holomorphic on a neighborhood of the spectrum σ(A) of A. For a solution X of that equation, norm estimates are established. By these estimates we investigate perturbations of a matrix A whose spectrum satisfies the condition . In the case with a positive integer ν we obtain conditions that provide localization of the spectrum of a perturbed matrix in a given angle. 相似文献
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