Variationally Asymptotically Stable Difference Systems

Choi, Sung Kyu; Goo, Yoon Hoe; Koo, Namjip

doi:10.1155/2007/35378

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…The notion of similarity is an effective tool to study the theory of stability for differential systems and difference systems [5,7,10,11,12,17,18,19]. Markus [17] introduced the notion of kinematic similarity in the set of all n × n continuous matrices defined on [t 0 , ∞) and showed that the relationship of kinematic similarity is an equivalence relation preserving the type numbers of the linear differential systems.…”

Section: Introductionmentioning

confidence: 99%

“…Trench [19] introduced summable similarity as a discrete analog of Conti's definition of t ∞ -similarity and investigated the various stabilities of linear difference systems by using summable similarity. Choi et al [5] studied the asymptotic property and the h-stability of difference systems via discrete similarities and comparison principle. For detailed results about the various stabilities including the notions of h-stability and strong stability of dynamic systems on time scales, see [6,8].…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic Equivalence Between Two Linear Dynamic Systems on Time Scales

Choi¹,

Koo²

2014

Bulletin of the Korean Mathematical Society

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Asymptotic Equivalence Between Two Linear Dynamic Systems on Time Scales

Choi¹,

Koo²

2014

Bulletin of the Korean Mathematical Society

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A new method for global h$$ h $$‐stability analysis for discrete‐time nonlinear systems with time‐varying delays

Zhang,

Yang

et al. 2024

Math Methods in App Sciences

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In this paper, we characterize the global ‐stability of discrete‐time nonlinear systems (DTNSs) with time‐varying delays. The global ‐stability encompasses several well‐known types of stability by using different choices of functions, such as global exponential stability (ES), Lagrange exponential stability (LES), and asymptotic stability. By exploiting a direct method based on the system solutions, we give a sufficient condition for the global ‐stability of the DTNSs in the form of simple inequalities that can be easily handled in MATLAB. Finally, numerical examples are presented to demonstrate the applicability of the method.

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Strong stability of optimal design to dynamic system for the fed-batch culture

et al. 2017

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Most economic and industrial processes are governed by inherently nonlinear dynamic system in which mathematical analysis (with few exceptions) is unable to provide general solutions; even the conditions to the existence of equilibrium point for the nonlinear dynamic system are simply not established in some special cases. In this paper, based on numerical solution of a nonlinear multi-stage automatic control dynamic (NMACD) in fed-batch culture of glycerol bioconversion to 1,3-propanediol (1,3-PD) induced by Klebsiella pneumoniae (K. pneumoniae), we consider an optimal design of the NMACD system. For convenience, the NMACD system is reconstructed together with the existence, uniqueness and continuity of solutions are discussed. Our goal is to prove the strong stability with respect to the perturbation of initial state for the solution to the NMACD system. To this end, we construct corresponding linear variational system for the solution to the NMACD system, and also prove the boundedness of fundamental matrix solutions to the linear variational system. On this basis, we prove the strong stability appearing above through the application of this boundedness.

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Variationally Asymptotically Stable Difference Systems

Cited by 3 publications

References 14 publications

Asymptotic Equivalence Between Two Linear Dynamic Systems on Time Scales

Asymptotic Equivalence Between Two Linear Dynamic Systems on Time Scales

A new method for global h$$ h $$‐stability analysis for discrete‐time nonlinear systems with time‐varying delays

Strong stability of optimal design to dynamic system for the fed-batch culture

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