Non-quadratic exponential stabilisation of non-linear hyperbolic partial differential equation systems

In this study, a new systematic approach is proposed to design the fuzzy controller for a class of Takagi–Sugeno fuzzy-partial differential equation (TS fuzzy-PDE) systems which describe the non-linear distributed parameter system formulated by first-order semi-linear hyperbolic PDEs. In this study,...

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Bibliographic Details
Published in:IET science, measurement & technology Vol. 8; no. 6; pp. 537 - 545
Main Authors: Sha Sadeghi, Mokhtar, Vafamand, Navid, Babaei, Mohammad Sadegh
Format: Journal Article
Language:English
Published: The Institution of Engineering and Technology 01.11.2014
Subjects:
asymptotic stability
control system synthesis
Design engineering
Design parameters
Differential equations
distributed parameter systems
first order semilinear hyperbolic PDE
Fuzzy control
fuzzy controller design
hyperbolic equations
linear matrix inequalities
LMI
Lyapunov functions
Lyapunov methods
nonlinear control systems
nonlinear differential equations
nonlinear distributed parameter system
nonlinear hyperbolic partial differential equation systems
Nonlinearity
nonquadratic exponential stabilisation
nonquadratic Lyapunov function
Partial differential equations
Stability
stability conditions
systematic approach
Takagi–Sugeno fuzzy partial differential equation
TS fuzzy‐PDE system
hyperbolic equations
fuzzy controller design
first order semilinear hyperbolic PDE
nonlinear distributed parameter system
nonquadratic Lyapunov function
nonlinear hyperbolic partial differential equation systems
control system synthesis
LMI
asymptotic stability
stability conditions
nonlinear differential equations
fuzzy control
linear matrix inequalities
nonlinear control systems
nonquadratic exponential stabilisation
distributed parameter systems
partial differential equations
TS fuzzy-PDE system
systematic approach
Lyapunov methods
Takagi–Sugeno fuzzy partial differential equation
ISSN:1751-8822, 1751-8830
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Summary:In this study, a new systematic approach is proposed to design the fuzzy controller for a class of Takagi–Sugeno fuzzy-partial differential equation (TS fuzzy-PDE) systems which describe the non-linear distributed parameter system formulated by first-order semi-linear hyperbolic PDEs. In this study, non-quadratic Lyapunov function is utilised and some slack matrices are introduced to derive stability conditions in terms of linear matrix inequalities (LMIs). The proposed approach has three main features. First, stability conditions are not derived in the form of spatial differential LMI. Second, conservativeness of LMI conditions is reduced. Third, there is no restriction on the form of semi-linear hyperbolic PDE systems and therefore more semi-linear systems classes can be stabilised. Also, the proposed approach is more suitable for practical implementation compared with the recently published papers.
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ISSN:1751-8822
1751-8830
DOI:10.1049/iet-smt.2014.0038