Stability analysis of T–S fuzzy models for nonlinear multiple time-delay interconnected systems

Chen, C. W.; Chiang, Wei-Ling; Hsiao, Feng‐Hsiag

doi:10.1016/j.matcom.2004.04.001

Cited by 116 publications

(52 citation statements)

References 14 publications

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“…Hence, in this study, we will measure the system entropy of SPDSs from the system's characteristics. Actually, many real physical and biological systems are only nonlinear, such as the large-scale systems [25][26][27][28], the multiple time-delay interconnected systems [29], the tunnel diode circuit systems [30,31], and the single-link rigid robot systems [32]. Therefore, we will also discuss the system entropy of nonlinear system as a special case in this paper.…”

Section: Introductionmentioning

confidence: 99%

System Entropy Measurement of Stochastic Partial Differential Systems

Chen

Hsieh

2016

Entropy

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System entropy describes the dispersal of a system's energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs) in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton-Jacobi integral inequality (HJII)-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs). To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs)-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3). Finally, several examples are presented to illustrate the system entropy measurement of SPDSs.

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Section: Introductionmentioning

confidence: 99%

System Entropy Measurement of Stochastic Partial Differential Systems

Chen

Hsieh

2016

Entropy

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“…Since linear models are utilized for the consequent parts, analysis using traditional system theory becomes straightforward. Several T-S fuzzy controllers have been described (for examples, see [3][4][5][6] and the references cited therein).…”

Section: Introductionmentioning

confidence: 99%

Stability analysis and robustness design of nonlinear systems: An NN-based approach

Chen

2011

Applied Soft Computing

105

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“…But in the process of modeling, disjoint decompositions may fail to transform the nonlinear system into a generalization of such a simple linear system. It is reasonable to assume that the produced T-S fuzzy system is composed of subsystems with connection [3]. Chiang et al proposed a stability criterion in terms of interconnected systems [3].…”

Section: Introductionmentioning

confidence: 99%

“…It is reasonable to assume that the produced T-S fuzzy system is composed of subsystems with connection [3]. Chiang et al proposed a stability criterion in terms of interconnected systems [3]. In Reference [2], the fuzzy system is viewed as an interconnection of subsystems, some of which are strongly connected, while others being weakly connected.…”

Section: Introductionmentioning

confidence: 99%

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Decentralized state observer scheme for uncertain time-delay T-S fuzzy interconnected systems

Zhang

Hou

Wang

2006

J. Control Theory Appl.

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This paper focuses on a class of T-S fuzzy interconnected systems with time delays and time-varying parameter uncertainties. Observer-based output feedback decentralized controller is designed such that the closed-loop interconnected system is asymptotically stable in the Lyapunov sense in probability for all admissible uncertainties and time delays. Sufficient conditions for robustly asymptotically stability of the systems are given in terms of a set of linear matrix inequalities (LMIs).

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Stability analysis of T–S fuzzy models for nonlinear multiple time-delay interconnected systems

Cited by 116 publications

References 14 publications

System Entropy Measurement of Stochastic Partial Differential Systems

System Entropy Measurement of Stochastic Partial Differential Systems

Stability analysis and robustness design of nonlinear systems: An NN-based approach

Decentralized state observer scheme for uncertain time-delay T-S fuzzy interconnected systems

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