Final-stability with some Applications

Lashiher, A. M. Ben; Storey, C.

doi:10.1093/imamat/9.3.397

Cited by 17 publications

(10 citation statements)

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“…The concept of nonvulnerability, which describes the system ability to withstand unpredictable, large, and continual disturbances, is of much practical importance (LaSdle and Lefschetz 1961;Lashiher and Storey 1972;Goh 1975Goh , 1976Holling 1973;Harrison 1979;Vincent and Anderson 1979;Vincent and Skowmnski 1980). This concept, which is closely related to the ideas of reachability and controllability in control systems theory (e.g.…”

Section: Vulnerabilitymentioning

confidence: 99%

A review of harvest theory and applications of optimal control theory in fisheries management

Cohen¹

1987

Can. J. Fish. Aquat. Sci.

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Management. Can. 1. Fish. Aqrmat. Sci. 44(Suppl. 2): 75-83.Optimal control theory is a useful tool for analysis of general mathematical models of fisheries and harvest strategies. It provides a framework for management decisions, but is too general for direct application to many specific management problems. A review of applications of optimal control theory to fisheries management is presented, with a general audience in mind. Advantages and shortcomings of optimal control theory in the context of fisheries management are discussed with some specific examples.La theorie du contr6le optimal constitue un outil utile pour I'analysede modeles mathematiques g6neraux des peches et des strategies d'exploitation. Elle fournit une base pour les dkcisions relatives a la gestion mais elle est trop generale pour 6tre appliquee directement a d e nornbreux probl&mes d e gestion determines. L'armteur presente, a I'intention du public, un examen des applications de cette theorie a la gestion haliermtique. II illustre a I'aide d'exemples ses avantages et ses inconvenients dans le contexte de la gestion haiieutique.In vector notation, (1) becomes wherex(t) is an n x 1 vector, representing the state of the system (e.g. species density), u(t) is an r x 1 input or control vector (e.g. harvest quota or harvest rate), and f is a vector-valued function. With time delays T, we have and for discrete systems, where k is the kth time interval.The optimal control problem is stated as follows: Given the state eq. (I), a set of boundary conditions on the state variables at the initial and terminal times, and a set of constraints on the state and control variables, determine the admissible controls u(t) so that a performance index (cost function) is minimized (or maximized). The boundiary conditions are given by x(to) and SEX($)] where to, 9, and S denote, respectively, the initial time, the final time, and the target set. Note that to is always fixed, but may be part sf the optimal control problem; e.g. one may strive to minimize rf:The performance index is expressed a% a scalar quantity where 6 and F are scalar-valued functions.The main theoretical approaches to the optimal-control-Can. J . Fish. Aquar. Sci., Vo%. 44, I987 7% Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by McMaster University on 11/25/14 For personal use only. Can. J . Fbh. A q u t . Sei., V01.44, 1987 Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by McMaster University on 11/25/14 For personal use only. (May 1974). When the ecosystem model is not large (e.g . m < 5), and when the parameters of F in (8) are not known, the Routh-Hunwitz stability criterion may be used to establish Can, 9. Fish. Aquat. Sci., VoI. 44, 1987 Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by McMaster University on 11/25/14For personal use only.

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Section: Vulnerabilitymentioning

confidence: 99%

A review of harvest theory and applications of optimal control theory in fisheries management

Cohen¹

1987

Can. J. Fish. Aquat. Sci.

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“…Many works have been published on this topic, with a particular focus on the Lyapunov's second method application, or on using matrix measure (see other works). Here, system stability analysis from the non‐Lyapunov point of view is studied . In addition, the linear time‐delay systems stability in the context of finite‐time stability was described and considered .…”

Section: Introductionmentioning

confidence: 99%

“…Here, system stability analysis from the non-Lyapunov point of view is studied. [6][7][8][9] In addition, the linear time-delay systems stability in the context of finite-time stability was described and considered. [10][11][12][13] In another context, the finite-time stability of neural network systems was investigated in related works.…”

Section: Introductionmentioning

confidence: 99%

Finite‐time stability of linear fractional‐order time‐delay systems

Naifar

Nagy

Makhlouf

et al. 2018

Intl J Robust & Nonlinear

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Summary In this paper, a finite‐time stability results of linear delay fractional‐order systems is investigated based on the generalized Gronwall inequality and the Caputo fractional derivative. Sufficient conditions are proposed to the finite‐time stability of the system with the fractional order. Numerical results are given and compared with other published data in the literature to demonstrate the validity of the proposed theoretical results.

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“…which includes many previous definitions of finite stability was introduced and considered by Grujić [7,8]. Concept of finite-time stability, called "final stability", was introduced by Lashirer and Story [9] and further development of these results was due to Lam and Weiss [10]. Also, analysis of linear time-delay systems in the context of finite and practical stability was introduced and considered by Debeljković and Lazarević [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Finite Time Stability Analysis of Linear Autonomous Fractional Order Systems With Delayed State

Lazarević¹,

Debeljković²

2008

Asian Journal of Control

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For the first time, in this paper, a stability test procedure is proposed for linear time‐invariant fractional order systems (LTI FOS). Paper extends some basic results from the area of finite time and practical stability to linear, continuous, fractional order time invariant time‐delay systems given in state space form. Sufficient conditions of this kind of stability, for particular class of fractional time‐delay systems is derived.

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Final-stability with some Applications

Cited by 17 publications

References 0 publications

A review of harvest theory and applications of optimal control theory in fisheries management

A review of harvest theory and applications of optimal control theory in fisheries management

Finite‐time stability of linear fractional‐order time‐delay systems

Finite Time Stability Analysis of Linear Autonomous Fractional Order Systems With Delayed State

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