Existence of Reachable and Observable Triples of Linear Discrete-Time Descriptor Systems

Moysis, Lazaros; Mishra, Vikas Kumar

doi:10.1007/s00034-018-0922-5

Cited by 6 publications

(5 citation statements)

References 30 publications

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“…x t + B 0 c t+n + R c w , 0 then c t 0 is obtained from (32). The specific result of the theorem follows for the choice w = 0 to achieve a production objective…”

Section: Reachability Properties Under the Non-singularity Constraint On The Re-usable Goods Substatementioning

confidence: 99%

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On the Reachability of a Feedback Controlled Leontief-Type Singular Model Involving Scheduled Production, Recycling and Non-Renewable Resources

2021

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This paper proposes and studies the reachability of a singular regular dynamic discrete Leontief-type economic model which includes production industries, recycling industries, and non-renewable products in an integrated way. The designed prefixed final state to be reached, under discussed reachability conditions, is subject to necessary additional positivity-type constraints which depend on the initial conditions and the final time for the solution to match such a final prescribed state. It is assumed that the model may be driven by both the demand and an additional correcting control in order to achieve the final targeted state in finite time. Formal sufficiency-type conditions are established for the proposed singular Leontief model to be reachable under positive feedback, correcting controls designed for appropriate demand/supply regulation. Basically, the proposed regulation scheme allows fixing a prescribed final state of economic goods stock in finite time if the model is reachable.

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“…x t + B 0 c t+n + R c w , 0 then c t 0 is obtained from (32). The specific result of the theorem follows for the choice w = 0 to achieve a production objective…”

Section: Reachability Properties Under the Non-singularity Constraint On The Re-usable Goods Substatementioning

confidence: 99%

“…The properties of positive and singular matrices or systems are discussed in [25][26][27][28][29][30][31]. Some useful techniques for factorization of M-matrices are found, for instance, in [32][33][34] and some of the references therein.…”

Section: Proposition 1 If I M − W Ymentioning

confidence: 99%

On the Reachability of a Feedback Controlled Leontief-Type Singular Model Involving Scheduled Production, Recycling and Non-Renewable Resources

2021

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“…In a real system, the discrete-time system often appears when only discrete data are available for use. Many discoveries about the discrete-time system were made by some researchers, see for example Dassios [9], Dassios and Kalogeropoulos [10], Oliva et al [8], Abraham and Kulkarni [23] and Moysis and Mishra [19].…”

Section: Introductionmentioning

confidence: 99%

“…Subcase1. If condition (19) holds for any agent i = 1, 2, then the solution to the variational inequality ( 12) is (18). Combining formulas ( 16) and ( 18), it is clearly known that…”

mentioning

confidence: 99%

Existence of an equilibrium for pure exchange economy with fuzzy preferences

Zhang,

Sun,

Jin

et al. 2020

Preprint

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This paper focuses on a new model to reach the existence of equilibrium in a pure exchange economy with fuzzy preferences (PXE-FP). The proposed model integrates exchange, consumption and the agent's fuzzy preference in the consumption set. We set up a new fuzzy binary relation on the consumption set to evaluate the fuzzy preferences. Also, we prove that there exists a continuous fuzzy order-preserving function in the consumption set under certain conditions. The existence of a fuzzy competitive equilibrium for the PXE-FP is confirmed through a new result on the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games. The payoffs of all strategy profiles for any agent are fuzzy numbers in fuzzy non-cooperative games. Finally, we show that the fuzzy competitive equilibrium could be characterized as a solution to an associated quasi-variational inequality, giving rise to an equilibrium solution.

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“…A considerable amount of literature has been published on the analysis of structural properties and more specifically on the reachability property (see [12], [13], [17], [23], [24], [32], [42] and [44]). In fact, it is still the subject of a detailed investigation (see [3], [5], [6], [15], [18], [22], [34], [35], [36], [40], [45] and [46], among others).…”

Section: Introductionmentioning

confidence: 99%

A first cubic upper bound on the local reachability index for some positive 2-D systems

Bailo

Gelonch

Romero‐Vivó

2019

RACSAM

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The calculation of the smallest number of steps needed to deterministically reach all local states of an nth-order positive 2-D system, which is called local reachability index (I LR ) of that system, was recently tackled by means of the use of a suitable composition table. The greatest index I LR obtained in the previous literature was n + 3 (⌊n/2⌋) 2 for some appropriated values of n. Taking as a basis both a combinatorial approach of such systems and the construction of suitable geometric sets in the plane, an upper bound on I LR depending on the dimension n for a new family of systems is characterized. The 2-D influence digraph of this family of order n ≥ 6 consists of two subdigraphs corresponding to a unique source s. The first one is a cycle involving the first n 1 vertices and is connected to the another subdigraph through the 1-arc (2, n 1 + n 2 ), being the natural numbers n 1 and n 2 such that n 1 > n 2 ≥ 2 and n − n 1 − n 2 ≥ 1. The second one has two main cycles, a cycle where only the remaining vertices n 1 + 1, . . . , n appear and a cycle containing only the vertices n 1 + 1, . . . , n 1 + n 2 − 1. Moreover, the last vertices are connected through the 2-arc (n 1 + n 2 − 1, n). Furthermore, if n ≥ 12 and is a multiple of 3, for appropriate n 1 and n 2 , the I LR of that family is at least

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Existence of Reachable and Observable Triples of Linear Discrete-Time Descriptor Systems

Cited by 6 publications

References 30 publications

On the Reachability of a Feedback Controlled Leontief-Type Singular Model Involving Scheduled Production, Recycling and Non-Renewable Resources

On the Reachability of a Feedback Controlled Leontief-Type Singular Model Involving Scheduled Production, Recycling and Non-Renewable Resources

Existence of an equilibrium for pure exchange economy with fuzzy preferences

A first cubic upper bound on the local reachability index for some positive 2-D systems

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