Robust Exponential Synchronization for a Class of Master-Slave Distributed Parameter Systems with Spatially Variable Coefficients and Nonlinear Perturbation Article Swipe

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Chengdong Yang , Jianlong Qiu , Kejia Yi , Xiangyong Chen , Ancai Zhang , Xiao Chen , Liuqing Yang ·

YOU? · · 2015 · Open Access · · DOI: https://doi.org/10.1155/2015/380903

This paper addresses the exponential synchronization problem of a class of master-slave distributed parameter systems (DPSs) with spatially variable coefficients and spatiotemporally variable nonlinear perturbation, modeled by a couple of semilinear parabolic partial differential equations (PDEs). With a locally Lipschitz constraint, the perturbation is a continuous function of time, space, and system state. Firstly, a sufficient condition for the robust exponential synchronization of the unforced semilinear master-slave PDE systems is investigated for all admissible nonlinear perturbations. Secondly, a robust distributed proportional-spatial derivative (P-sD) state feedback controller is desired such that the closed-loop master-slave PDE systems achieve exponential synchronization. Using Lyapunov’s direct method and the technique of integration by parts, the main results of this paper are presented in terms of spatial differential linear matrix inequalities (SDLMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed methods applied to the robust exponential synchronization problem of master-slave PDE systems with nonlinear perturbation.

Related Topics

Mathematics

Lipschitz Continuity

Partial Differential Equation

Mathematical Analysis

Computer Science

Physics

Artificial Intelligence

Combinatorics

Quantum Mechanics

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Mathematics Nonlinear system Lipschitz continuity Perturbation (astronomy) Exponential function Control theory (sociology) Applied mathematics Partial differential equation Synchronization (alternating current) Exponential decay Mathematical analysis Computer science Topology (electrical circuits) Physics Control (management) Nuclear physics Artificial intelligence Combinatorics Quantum mechanics

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Type: article
Language: en
Landing Page: https://doi.org/10.1155/2015/380903
PDF: https://downloads.hindawi.com/journals/mpe/2015/380903.pdf
OA Status: hybrid
Cited By: 9
References: 42
Related Works: 10
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DOI: https://doi.org/10.1155/2015/380903

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Title: Robust Exponential Synchronization for a Class of Master-Slave Distributed Parameter Systems with Spatially Variable Coefficients and Nonlinear Perturbation

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Language: en

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Publication year: 2015

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Publication date: 2015-01-01

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Authors: Chengdong Yang, Jianlong Qiu, Kejia Yi, Xiangyong Chen, Ancai Zhang, Xiao Chen, Liuqing Yang

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Landing page: https://doi.org/10.1155/2015/380903

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Concepts: Mathematics, Nonlinear system, Lipschitz continuity, Perturbation (astronomy), Exponential function, Control theory (sociology), Applied mathematics, Partial differential equation, Synchronization (alternating current), Exponential decay, Mathematical analysis, Computer science, Topology (electrical circuits), Physics, Control (management), Nuclear physics, Artificial intelligence, Combinatorics, Quantum mechanics

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Cited by: 9

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