Control synthesis of Roesser type discrete-time 2-D T–S fuzzy systems via a multi-instant fuzzy state-feedback control scheme

Xie, Xiangpeng; Zhang, Zhiwen; Hu, Songlin

doi:10.1016/j.neucom.2014.10.051

Cited by 22 publications

(6 citation statements)

References 28 publications

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“…By analogy, with the assistance of the product inference engine, the singleton fuzzifier, and the center average defuzzifier, 27,28 the overall dynamics of the T‐S fuzzy system () can be reflected as:

\{\begin{matrix} x false(k + 1 false) = true \sum_{i = 1}^{t} h_{i} false(ι false(k false) false) false[A_{i} x false(k false) + D_{i} v false(k false) + G_{i} f false(k false) false], \\ y false(k false) = true \sum_{i = 1}^{t} h_{i} false(ι false(k false) false) false[C_{i} x false(k false) + E_{i} v false(k false) false], \end{matrix}

where

h_{i} (ι (k))

is the fuzzy basis function defined as follows:

h_{i} (ι (k)) = \frac{ϱ_{i} (ι (k))}{\sum_{i = 1}^{t} ϱ_{i} (ι (k))}, ϱ_{i} (ι (k)) = \prod_{i = 1}^{p} α_{i j} (ι_{j} (k)),

with

α_{i <...>}

…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Nonfragile H_∞ fault detection for fuzzy discrete systems under stochastic communication protocol

Ren

Sun

Huo

et al. 2020

Optim Control Appl Methods

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SummaryIn this article, considering one type of fuzzy discrete‐time networked control systems (NCSs) under stochastic communication protocol (SCP), a fuzzy‐based nonfragile H∞ filter is developed to detect the subsistent fault signal. The Takagi‐Sugeno (T‐S) mathematical model is employed to approximate the nonlinearities in the concerned fuzzy NCSs. The SCP is adopted to decide which sensor gets the access to the communication network at certain time instant, and the scheduling model of which is constructed as a Markov chain. Taking into account that the filter gain parameters in real practice may suffer fluctuations during the implementation, a modified nonfragile fuzzy filter is designed to detect the fault occurred in the signal transmission. By using the strong centralized stochastic analysis technique and the matrix calculation method, a Lyapunov function is adopted to derive sufficient conditions under which the filtering error dynamics is stochastically stable and the H∞ performance is satisfied. Then, the desired nonfragile fuzzy fault detection filter is realized by solving a certain linear matrix inequality. Finally, the effectiveness of the develop fault detection scheme is verified in the simulation example.

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\{\begin{matrix} x false(k + 1 false) = true \sum_{i = 1}^{t} h_{i} false(ι false(k false) false) false[A_{i} x false(k false) + D_{i} v false(k false) + G_{i} f false(k false) false], \\ y false(k false) = true \sum_{i = 1}^{t} h_{i} false(ι false(k false) false) false[C_{i} x false(k false) + E_{i} v false(k false) false], \end{matrix}

where

h_{i} (ι (k))

is the fuzzy basis function defined as follows:

h_{i} (ι (k)) = \frac{ϱ_{i} (ι (k))}{\sum_{i = 1}^{t} ϱ_{i} (ι (k))}, ϱ_{i} (ι (k)) = \prod_{i = 1}^{p} α_{i j} (ι_{j} (k)),

with

α_{i <...>}

…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Nonfragile H_∞ fault detection for fuzzy discrete systems under stochastic communication protocol

Ren

Sun

Huo

et al. 2020

Optim Control Appl Methods

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“…For control purpose, the 2-D T-S system is discretized with sampling intervals T 1 and T 2 corresponding to variables x and t, respectively, with the system parameters given in Xiang-Peng and Zhang (2010a, b) and Xie et al (2015), obtaining the following system:…”

Section: Computer Simulationsmentioning

confidence: 99%

Control of Discrete 2-D Takagi–Sugeno Systems via a Sum-of-Squares Approach

Chaibi

Hmamed

Tissir

et al. 2019

J Control Autom Electr Syst

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The stabilization of Takagi-Sugeno systems is solved here for the two-dimensional polynomial discrete case, by using the sum-of-squares approach. First, we provide a stabilization condition formulated in terms of polynomial multiple Lyapunov functions. Then, a non-quadratic stabilization condition is developed by applying relaxed stabilization technique. Both conditions can be used for design, by solving them using numerical tools such as SOSTOOLS. A numerical example illustrates the effectiveness of the results.

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“…The study of two-dimensional systems has a long history, with some meaningful works (Roesser, 1975;Fornasini & Marchesini, 1976;Lin & Bruton, 1989;Lu & Antoniou, 1992;Xu et al, 2005;Hu & Liu, 2006;Singh, 2014;Xie et al, 2015;Ahn et al, 2016) such as systems theory, stability properties and practical applications. Among all research topics of two-dimensional systems, stability as the most fundamental property has obtained fruitful achievements.…”

Section: Introductionmentioning

confidence: 99%

Finite-region boundedness and stabilization for 2D continuous-discrete systems in Roesser model

Hua

Wang

et al. 2018

IMA Journal of Mathematical Control and Information

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This paper investigates the finite-region boundedness (FRB) and stabilization problems for two-dimensional continuous-discrete linear Roesser models subject to two kinds of disturbances. For two-dimensional continuous-discrete system, we first put forward the concepts of finite-region stability and FRB. Then, by establishing special recursive formulas, sufficient conditions of FRB for two-dimensional continuous-discrete systems with two kinds of disturbances are formulated. Furthermore, we analyze the finite-region stabilization issues for the corresponding two-dimensional continuous-discrete systems and give generic sufficient conditions and sufficient conditions that can be verified by linear matrix inequalities for designing the state feedback controllers which ensure the closed-loop systems FRB. Finally, viable experimental results are demonstrated by illustrative examples.

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Control synthesis of Roesser type discrete-time 2-D T–S fuzzy systems via a multi-instant fuzzy state-feedback control scheme

Cited by 22 publications

References 28 publications

Nonfragile H_∞ fault detection for fuzzy discrete systems under stochastic communication protocol

Nonfragile H_∞ fault detection for fuzzy discrete systems under stochastic communication protocol

Control of Discrete 2-D Takagi–Sugeno Systems via a Sum-of-Squares Approach

Finite-region boundedness and stabilization for 2D continuous-discrete systems in Roesser model

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Control synthesis of Roesser type discrete-time 2-D T–S fuzzy systems via a multi-instant fuzzy state-feedback control scheme

Cited by 22 publications

References 28 publications

Nonfragile H∞ fault detection for fuzzy discrete systems under stochastic communication protocol

Nonfragile H∞ fault detection for fuzzy discrete systems under stochastic communication protocol

Control of Discrete 2-D Takagi–Sugeno Systems via a Sum-of-Squares Approach

Finite-region boundedness and stabilization for 2D continuous-discrete systems in Roesser model

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Nonfragile H_∞ fault detection for fuzzy discrete systems under stochastic communication protocol

Nonfragile H_∞ fault detection for fuzzy discrete systems under stochastic communication protocol