The Experts below are selected from a list of 291 Experts worldwide ranked by ideXlab platform
Hua Shao - One of the best experts on this subject based on the ideXlab platform.
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Some criteria of chaos in non-autonomous Discrete Systems
arXiv: Dynamical Systems, 2019Co-Authors: Hua Shao, Guanrong ChenAbstract:This paper establishes some criteria of chaos in non-autonomous Discrete Systems. Several criteria of strong Li-Yorke chaos are given. Based on these results, some criteria of distributional chaos in a sequence are established. Moreover, several criteria of distributional chaos induced by coupled-expansion for an irreducible transition matrix are obtained. Some of these results not only extend the existing related results for autonomous Discrete Systems to non-autonomous Discrete Systems, but also relax the assumptions of the counterparts. One example is provided for illustration.
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Lyapunov Exponents, Sensitivity, and Stability for Non-Autonomous Discrete Systems
International Journal of Bifurcation and Chaos, 2018Co-Authors: Hua ShaoAbstract:This paper focuses on the relationships of Lyapunov exponents with sensitivity and stability for non-autonomous Discrete Systems. Some new concepts are introduced for non-autonomous Discrete Systems, including Lyapunov exponents, strong sensitivity at a point and in a set, Lyapunov stability, and exponential asymptotical stability. It is shown that the positive Lyapunov exponent at a point implies strong sensitivity for a class of non-autonomous Discrete Systems. Furthermore, the uniformly positive Lyapunov exponents in a totally invariant set imply strong sensitivity in this set under certain conditions. The negative Lyapunov exponent at a point implies exponential asymptotical stability for a class of non-autonomous Discrete Systems. The related existing results for autonomous Discrete Systems are generalized to non-autonomous Discrete Systems and their conditions are weakened. One example is provided for illustration.
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Lyapunov Exponents, Sensitivity, and Stability for Non-Autonomous Discrete Systems
International Journal of Bifurcation and Chaos, 2018Co-Authors: Hua ShaoAbstract:This paper focuses on the relationships of Lyapunov exponents with sensitivity and stability for non-autonomous Discrete Systems. Some new concepts are introduced for non-autonomous Discrete system...
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Devaney Chaos in Nonautonomous Discrete Systems
International Journal of Bifurcation and Chaos, 2016Co-Authors: Hua ShaoAbstract:This paper is concerned with Devaney chaos in nonautonomous Discrete Systems. It is shown that in its definition, the two former conditions, i.e. transitivity and density of periodic points, in a set imply the last one, i.e. sensitivity, in the case that the set is unbounded, while a similar result holds under two additional conditions in the other case that the set is bounded. Some chaotic behavior is studied for a class of nonautonomous Discrete Systems, each of which is governed by a convergent sequence of continuous maps. In addition, the concepts of some pseudo-orbits and shadowing properties are introduced for nonautonomous Discrete Systems, and it is shown that some shadowing properties of the system and density of periodic points imply that the system is Devaney chaotic under the condition that the sequence of continuous maps is uniformly convergent in a compact metric space.
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Lyapunov exponents, sensitivity, and stability for non-autonomous Discrete Systems
arXiv: Dynamical Systems, 2016Co-Authors: Hua ShaoAbstract:This paper is concerned with relationships of Lyapunov exponents with sensitivity and stability for non-autonomous Discrete Systems. Some new concepts are introduced for non-autonomous Discrete Systems, including Lyapunov exponents, strong sensitivity at a point and in a set, Lyapunov stability, and exponential asymptotical stability. It is shown that the positive Lyapunov exponent at a point implies strong sensitivity for a class of non-autonomous Discrete Systems. Furthermore, the uniformly positive Lyapunov exponents in a totally invariant set imply strong sensitivity in this set under certain conditions. It is also shown that the negative Lyapunov exponent at a point implies exponential asymptotical stability for a class of non-autonomous Discrete Systems. The related existing results for autonomous Discrete Systems are generalized to non-autonomous Discrete Systems and their conditions are weaken. One example is provided for illustration.
P. Agathoklis - One of the best experts on this subject based on the ideXlab platform.
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Algebraic necessary and sufficient conditions for the stability of 2-D Discrete Systems
1991. IEEE International Sympoisum on Circuits and Systems, 1991Co-Authors: P. Agathoklis, E.i. Jury, Mohamed MansourAbstract:Algebraic necessary and sufficient conditions for the stability analysis of 2-D Discrete Systems are presented. These conditions are developed based on the frequency-dependent formulation of the Lyapunov equation using Kronecker products. It is shown that these necessary and sufficient conditions for internal stability of 2-D Discrete Systems are equivalent to testing the eigenvalues of constant matrices. This is a simplification over earlier tests which require testing the positivity of one or more functions of omega for all omega epsilon (0,2 pi ).
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Discrete Systems reduction via impulse-response Grammians and its relation to q-Markov covers
IEEE International Symposium on Circuits and Systems, 1990Co-Authors: V. Sreeram, P. AgathoklisAbstract:A new method for model reduction of linear Discrete Systems is proposed. It is based on the impulse-response Grammian proposed for Discrete Systems. This Grammian is an extension of the one proposed for linear continuous Systems and contains information on the input-output behavior of the system. The rth-order reduced-order models are made to retain the first r Markov parameters and the first r*r elements of the impulse-response Grammian of the original system. The relation between this method and the q-Markov cover method is discussed.
Yang Xiao - One of the best experts on this subject based on the ideXlab platform.
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Stability test for 2-D continuous-Discrete Systems
Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), 2001Co-Authors: Yang XiaoAbstract:Models of 2-D continuous-Discrete Systems are considered, which can be used to describe some complex Systems. Different from classical 2-D continuous Systems or 2-D Discrete Systems, the asymptotic stability of continuous-Discrete Systems is determined by Hurwitz-Schur stability (hybrid one) of 2-D characteristic polynomials of the Systems. An algebraic algorithm with simpler test procedure for Hurwitz-Schur stability test of 2-D polynomials is developed. An example to illustrate the application of the test approach is provided.
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Finite state test for asymptotic stability of two-dimensional shift-variant Discrete Systems
WCC 2000 - ICSP 2000. 2000 5th International Conference on Signal Processing Proceedings. 16th World Computer Congress 2000, 2000Co-Authors: Yang XiaoAbstract:Test theorems and their algorithms for asymptotic stability test of two-dimensional (2-D) shift-variant Discrete Systems are presented and proved. Compared with the classical results about stability of 1-D shift-variant Discrete Systems, our criteria are based on finite states of system matrices of the shift-variant Discrete Systems, and they are necessary and sufficient conditions for asymptotic stability of 1-D and 2-D shift-variant Discrete Systems. The criteria are of simpler forms for their on-line applications. Examples are given to illustrate the difference of stability criteria between shift-variant Discrete Systems and shift-invariant Discrete Systems.
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The Stability of Discrete Systems with Variable Time
Journal of Changsha Communications University, 1999Co-Authors: Yang XiaoAbstract:The author of this essay has researched the stability of Discrete Systems with variable time and provided some algebraic conditions for uniform stability of the zero solution of linear and non linear Discrete Systems with variable time by using maximal Liapunov function method.
T.w.s. Chow - One of the best experts on this subject based on the ideXlab platform.
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Iterative learning control for linear time-variant Discrete Systems based on 2-D system theory
IEE Proceedings - Control Theory and Applications, 2005Co-Authors: X.-d. Li, J.k.l. Ho, T.w.s. ChowAbstract:The two-dimensional (2-D) system theory iterative learning control (ILC) techniques for linear time-invariant Discrete Systems are extended to the cases of linear time-variant Discrete Systems. By exploiting the convergent property of 2-D linear time-variant Discrete Systems with only one independent variable, a kind of 2-D system theory ILC approach is presented for linear time-variant Discrete Systems. Sufficient conditions are given for convergence of the proposed ILC rules. Two numerical examples are used to validate the ILC procedures.
N. Theodorou - One of the best experts on this subject based on the ideXlab platform.
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Computation of the stability margin of two-dimensional Discrete Systems
IEEE Transactions on Automatic Control, 1992Co-Authors: A. Kanellakis, S. Tzafestas, N. TheodorouAbstract:Two methods of computing the stability margin of two-dimensional Discrete Systems are presented. The first method uses the Schur-Cohn stability criterion, and the second method is based on results concerning the 1-D Lyapunov equation with complex coefficients. Several examples illustrate the applicability of the two methods.
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Method for computing the stability margin of 2-D Discrete Systems
Electronics Letters, 1990Co-Authors: S. Tzafestas, A. Kanellakis, N. TheodorouAbstract:A method to compute the stability margin of 2-D Discrete Systems described in state-space is presented. This method is based on results on the 1-D Lyapunov equation with complex coefficients.