Membership-function-dependent stability analysis of fuzzy-model-based control systems using fuzzy Lyapunov functions

Lam, Hak‐Keung; Lauber, Jimmy

doi:10.1016/j.ins.2012.12.027

Cited by 80 publications

(43 citation statements)

References 42 publications

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“…Recently, the TS fuzzy model has been widely employed for the analysis and synthesis of non-linear ODE systems [26,27,36] and non-linear parabolic PDE systems [30][31][32][33]. In this section, a TS fuzzy hyperbolic PDE model is presented to accurately represent the non-linear hyperbolic PDE system [1,35].…”

Section: Ts Fuzzy-pde Modelmentioning

confidence: 99%

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

Sadeghi

Vafamand

Babaei

2014

IET Science, Measurement & Technology

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In this study, a new systematic approach is proposed to design the fuzzy controller for a class of Takagi-Sugeno fuzzypartial 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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Section: Ts Fuzzy-pde Modelmentioning

confidence: 99%

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

Sadeghi

Vafamand

Babaei

2014

IET Science, Measurement & Technology

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“…In T-S fuzzy model, some local linear systems can be interpolated by the so-called membership functions in a unit framework. In the past few decades, the problem of stability analysis and controller synthesis by the utilization of T-S fuzzy models has been widely investigated (see, for example, Feng, 3 Liu et al, 4 Su et al, 5 Lam and Lauber, 6 Liu et al, 7 Wu et al, 8 and Wei et al 9 and references therein). As an impactful control methodology in control systems, passivity control has been successfully applied in engineering applications, such as electrical circuit systems, mechanical systems, and complex network systems.…”

Section: Introductionmentioning

confidence: 99%

Memory-based passive control design for complex networked fuzzy delta operator systems

Zhao

Yan

Shen

2017

Advances in Mechanical Engineering

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This article investigates the memory-based state-feedback control with strict passivity performance for nonlinear systems in delta domain. Takagi-Sugeno fuzzy model of delta operator form is adopted as an approximator of the investigated nonlinear plant with system perturbations/exogenous disturbances. The nonlinear output of the plant, which is accompanied with complex exogenous disturbances, is formulated as the passive output satisfying a pre-designed strict passivity performance. The memory-based state-feedback controller is expressed with a known memory coefficient to significant the influence of the delayed states. The resulting closed-loop system is inferred as a time-varying delay system, of which the stability and passivity criterion is carried out via a general fuzzy Lyapunov-Krasovskii functional approach. Then, parametric gains of the desired strictly passive memory-based controller are designed subject to a set of solvable matrix inequalities. Finally, a numerical example shows the validity of the proposed memory-based passive control method.

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“…The first method of reducing the conservativeness is considering the permutations of membership functions in the fuzzy summations [9], [10], which can be handled generally by Pólya's theory in [11]. The second approach is exploiting different Lyapunov function candidates such as quadratic Lyapunov function [5], piecewise linear Lyapunov function [12], switching Lyapunov function [13], [14], fuzzy Lyapunov function [15], [16] and polynomial Lyapunov function [14], [17]. The third method is obtaining membershipfunction-dependent stability conditions.…”

Section: Introductionmentioning

confidence: 99%

“…By bringing the information of membership functions into stability analysis, the stability conditions will depend on particular shapes of membership functions rather than any shapes. This approach includes polynomial constraints [18], symbolic variables [3], [19], [20], approximated membership functions [21], [22] and others [16]. During the relaxation process, slack matrices are added to stability conditions through S-procedure [23], which brings more freedom for satisfying the conditions.…”

Section: Introductionmentioning

confidence: 99%

Control of nonlinear systems by fuzzy observer-controller with unmeasurable premise variables

Liu

Lam

Tsai

et al. 2015

2015 International Conference on Advanced Robotics and Intelligent Systems (ARIS)

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Abstract-In this paper, we investigate the stability of TakagiSugeno (T-S) fuzzy-model-based (FMB) observer-control system. Premise membership functions depending on unmeasurable premise variables are considered to enhance the flexibility and applicability of the fuzzy observer-controller. The fuzzy observer is designed to estimate the system states and the estimated states are employed for state-feedback control of nonlinear systems. Convex stability conditions are obtained through matrix decoupling technique so that a solution can be searched using convex programming techniques. The proposed analysis is able to reduce the number of predefined scalars by adequately choosing the augmented vector. Nonetheless, due to the mismatched premise membership functions between the fuzzy model and fuzzy observer-controller, it complicates the stability analysis which potentially leads to conservative stability conditions. To alleviate the problem, the stability conditions are relaxed by membershipfunction-dependent approach which takes the information of membership functions into consideration in the stability analysis. Simulation examples are provided to demonstrate the feasibility and relaxation of proposed FMB observer-control scheme.

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Membership-function-dependent stability analysis of fuzzy-model-based control systems using fuzzy Lyapunov functions

Cited by 80 publications

References 42 publications

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

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

Memory-based passive control design for complex networked fuzzy delta operator systems

Control of nonlinear systems by fuzzy observer-controller with unmeasurable premise variables

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