Variable structure control for a singular biological economic model with time delay and stage structure

Zhang, Yi; Wei, Yudan

doi:10.1186/s13662-017-1436-3

Cited by 3 publications

(4 citation statements)

References 20 publications

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“…Singular system has been widely investigated since it can describe various fields, to mention a few, information technology, electricity, physics, chemistry, biology and economy [1]- [5]. Compared with normal system, singular system has complicated feature, e.g., impulsiveness is one of the characteristics.…”

Section: Introductionmentioning

confidence: 99%

“…Compared with normal system, singular system has complicated feature, e.g., impulsiveness is one of the characteristics. It is worth noticing that singular system can model biodynamic systems [1]- [4]. With the development of the theory about T-S fuzzy system, [1] studied the control problem of a class of bioeconomic models with H ∞ performance.…”

Section: Introductionmentioning

confidence: 99%

“…It is worth noticing that singular system can model biodynamic systems [1]- [4]. With the development of the theory about T-S fuzzy system, [1] studied the control problem of a class of bioeconomic models with H ∞ performance. The problem of bifurcation and control for biological economic system has been considered in [2] and [3].…”

Section: Introductionmentioning

confidence: 99%

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Sliding Mode Control for Uncertain T-S Fuzzy Singular Biological Economic System

Zhang

Shi

2019

IEEE Access

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In this paper, the design of sliding mode controller for a singular biological economic model with a stage structure and uncertain parameters is studied. First, a biological economic system with uncertain parameters for the invasion of alien species is modeled by a singular system. Then, according to the theory of the T-S fuzzy system, an uncertain T-S fuzzy singular model is established and the stability of the model at the positive equilibria is discussed. Furthermore, a fuzzy integral sliding surface and a sliding mode controller are designed for the T-S fuzzy singular system with an uncertain term. At the same time, the state trajectories can be driven onto the integral sliding surface in finite time and a sufficient condition about the global asymptotic stability of sliding motion is obtained. Finally, a simulation is given to verify the effectiveness of the obtained results. INDEX TERMS The invasion of alien species, Positive equilibria, sliding mode controller, global asymptotic stability.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sliding Mode Control for Uncertain T-S Fuzzy Singular Biological Economic System

Zhang

Shi

2019

IEEE Access

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“…Their ideas originate from the economic theory in [5]: Net Economic Profit = Total Revenue -Total Cost. Bioeconomic models with invasion of alien species have been developed in [6]. In fact, we all know that the population is divided into stages in the whole growth process and will be affected by the external environment.…”

Section: Introductionmentioning

confidence: 99%

Sliding Mode Observer-Based Control for Uncertain Singular Biological Economic System With Invasion of Alien Species

Shi

Zhang

2019

IEEE Access

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In this paper, the controller based on sliding mode observer (SMO) is studied for a singular biological economic model with stage structure and uncertain parameters. First, a biological economic system is established by the singular system with uncertain parameters for the invasion of alien species. And SMO is designed by use of control inputs and measurement outputs. Then, the integral sliding surface is constructed for the error system and the SMO system. Second, by constructing an augmented system, it is ensured that the system is regular, free of impulse, and stable by use of the linear matrix inequality technique and Lyapunov stability theory. Third, a sliding mode control (SMC) law is designed to guarantee the considered system reaching the sliding mode surface. Finally, the effectiveness of the proposed method is illustrated by a simulation example. INDEX TERMS Stage structure, singular biological economic system, sliding mode observer. 91548 VOLUME 7, 2019 Z. Shi et al.: SMO-Based Control for Uncertain Singular Biological Economic System Let z 1 (t) = −(a 1 + b + b) − c 1 x 1 (t), z 2 (t) = −a 2 − c 2 x 2 (t), z 3 (t) = −x 2 (t), z 4 = pE 1 (t). So max z 1 (t) = −(a 1 + b + b) − c 1 x 1 min (t), min z 1 (t) = −(a 1 + b + b) − c 1 x 1 max (t), max z 2 (t) = −a 2 − c 2 x 2 min (t), min z 2 (t) = −a 2 − c 2 x 2 max (t), max z 3 (t) = −x 2 min (t), min z 3 (t) = −x 2 max (t), max z 4 = pE 1 max (t), min z 4 = pE 1 min (t). Using the maximum and minimum values, z 1 (t) , z 2 (t) , z 3 (t) and z 4 (t) can be represented by z 1 (t) = M 11 (z 1 (t)) max z 1 (t) + M 12 (z 1 (t)) min z 1 (t) , z 2 (t) = M 21 (z 2 (t)) max z 2 (t) + M 22 (z 2 (t)) min z 2 (t) , z 3 (t) = M 31 (z 3 (t)) max z 3 (t) + M 32 (z 3 (t)) min z 3 (t) , z 4 (t) = M 41 (z 4 (t)) max z 4 (t) + M 42 (z 4 (t)) min z 4 (t) .

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Existence and Stability of Pseudo Almost Periodic Solutions for a Delayed Multispecies Logarithmic Population Model with Feedback Control

Xia

Deng

2021

Qual. Theory Dyn. Syst.

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Variable structure control for a singular biological economic model with time delay and stage structure

Cited by 3 publications

References 20 publications

Sliding Mode Control for Uncertain T-S Fuzzy Singular Biological Economic System

Sliding Mode Control for Uncertain T-S Fuzzy Singular Biological Economic System

Sliding Mode Observer-Based Control for Uncertain Singular Biological Economic System With Invasion of Alien Species

Existence and Stability of Pseudo Almost Periodic Solutions for a Delayed Multispecies Logarithmic Population Model with Feedback Control

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