On relaxed LMI-based designs for fuzzy regulators and fuzzy observers

Teixeira, Marcelo Carvalho Minhoto; Assunção, Edvaldo; Pietrobom, Hilton Cleber

doi:10.23919/ecc.2001.7075892

Cited by 34 publications

(63 citation statements)

References 10 publications

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“…Since then, the T-S FMB control systems have drawn the attention of fuzzy control researchers for more than 20 years due to its effectiveness on handling nonlinear control systems [7,8]. In particular, the issues of stability analysis and control synthesis have been investigated extensively and fruitful results can be found in [2,[9][10][11][12][13][14][15][16][17][18][19] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

“…The PLMFs carrying the information of the original membership functions can be brought into the stability conditions so that the stability conditions become membership-function dependent. It implies that the stability conditions are dedicated to the FMB control system with specific membership functions to be handled and thus more relaxed stability results can be obtained compared with membership-function-independent analysis results [2,[9][10][11][12][13][14][15][16]. Furthermore, we consider a cost function to describe the system performance on top of the stability analysis.…”

Section: Introductionmentioning

confidence: 99%

“…The work in [10] used the symmetry property of the membership functions of the T-S fuzzy model and fuzzy controller in the analysis and then managed to relax the LMI-based stability conditions. Inspired by the work in [10], various techniques have been proposed to gather the membership functions in the stability analysis [2,[11][12][13][14][15]. The work in [11] combined all the LMIs used in [10] to form a large symmetric matrix resulting in further reducing the conservativeness of stability conditions.…”

Section: Introductionmentioning

confidence: 99%

“…If there exists a common solution of a group of Lyapunov inequalities in terms of LMIs which can be solved effectively by convex optimization methods such as interior point method [2], the FMB control system is guaranteed to be asymptotically stable [9]. With the parallel distribution compensation (PDC) [9] design approach, the stability conditions can be relaxed and some further related works can be found in [2,[9][10][11][12][13][14][15][16]. The work in [10] used the symmetry property of the membership functions of the T-S fuzzy model and fuzzy controller in the analysis and then managed to relax the LMI-based stability conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Under the PDC design technique [2,[9][10][11][12][13][14][15][16], both the T-S fuzzy model and fuzzy controller are required to share the same set of premise rules (the same premise variables, number of rules, and membership functions), which limits the flexibility of the controller design and as well as unnecessarily increase the complexities of the controller in some cases. However, if the premise rules of the fuzzy controller are different from those of the T-S fuzzy model, the stability analysis results will be very conservative as the permutations of the membership functions used in the PDC design cannot be applied due to the mismatched premised membership functions.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Membership-Function-Dependent Stability Analysis and Control Synthesis of Guaranteed Cost Fuzzy-Model-Based Control Systems

Lam

Xiao

et al. 2016

Int. J. Fuzzy Syst.

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This paper focuses on the guaranteed cost stability analysis of fuzzy-model-based (FMB) control systems. Representing the nonlinear plant using a TakagiSugeno (T-S) fuzzy model, a fuzzy controller is employed to close the feedback loop. A weighted linear quadratic cost function is considered as the cost index to measure the performance of the closed-loop fuzzy system in terms of the system states, system outputs, and control signals. The stability of the FMB control system is investigated by the Lyapunov stability theory subject to the minimization of cost index for performance realization. A membershipfunction-dependent approach using the piecewise-linear membership functions is employed to include the information of membership functions into the stability analysis. Membership-function-dependent stability conditions in terms of linear matrix inequalities are obtained to determine the system stability and feedback gains with the consideration of the system performance measured by the cost function. A simulation example is provided to illustrate the effectiveness and merits of the proposed approach.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Membership-Function-Dependent Stability Analysis and Control Synthesis of Guaranteed Cost Fuzzy-Model-Based Control Systems

Lam

Xiao

et al. 2016

Int. J. Fuzzy Syst.

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Smoothing switched control laws for uncertain nonlinear systems subject to actuator saturation

Alves

Teixeira

Oliveira

et al. 2016

Adaptive Control & Signal

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This paper considers a class of uncertain nonlinear systems exactly described by Takagi-Sugeno (T-S) fuzzy models, with or without matched uncertainties and/or disturbances, within an operating region in the state space. Considering the plant subject to actuator saturation is proposed, a switched control design method such that the equilibrium point of the controlled systems is locally asymptotically stable with an adequate decay rate, for all initial conditions in a region obtained in the design procedure, that is within a given operating region. Moreover, an exact representation of the minimum function using signal functions is presented. Therefore, it is offered a bridge between the switched control and variable structure control laws, because they are usually based on minimum and signal functions, respectively. Considering the well-known approximation of the signal function by a sigmoid function, this paper introduces the 'smooth minimum' function. The smooth minimum function allowed the design of 'smooth switched' control laws, without chattering, for the aforementioned class of systems. The proposed smooth switched control laws guarantee the uniform ultimate boundedness of the controlled systems. Design examples and simulation results illustrate the control design procedures and the effectiveness of the proposed control laws. Future researches in this subject may explore the presented relationship between the switched control and variable structure control laws, in order to obtain new useful control laws. of the system by choosing a feedback gain, belonging to a given set of gains, which minimizes the time derivative of a Lyapunov function. The design conditions are represented by LMIs, which can be solved in a computationally efficient manner [15,16].Frequent and/or abrupt changes of the feedback gains, however, can generate control signal chattering. Control signal chattering is a generally undesirable phenomenon in real systems. Different control strategies try to avoid the chattering problem, for instance, in sliding mode control [17][18][19][20][21][22][23][24], to name a few, in adaptive control [25][26][27], and in control of switched linear systems [28][29][30].In this context, this paper extends the methodology proposed in [13,14] for uncertain T-S fuzzy models, based on [31,32], taking into account actuators saturation. Additionally, an invariant region E.P; 1/ is estimated, in which for every x.0/ 2 E.P; 1/, the state vector of the controlled system x.t/, t > 0 is in a given operation region where the T-S fuzzy model exactly describes the nonlinear system and also the equilibrium point of the controlled systems is locally asymptotically stable with an adequate decay rate. Moreover, 'smooth switched' control laws are proposed, without using the plant membership functions. A key point of the new control laws is a proposed exact representation of the minimum function using signal functions. Considering that the minimum functions are largely used in switched control laws [13,14,[28][29][30] and the s...

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Poly‐quadratic stability of discrete‐time nonlinear systems in Takagi‐Sugeno's form

Ding

2009

Asian Journal of Control

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This paper studies poly‐quadratic stability of nonlinear systems represented by a Takagi‐Sugeno (T‐S) discrete fuzzy model. A system is poly‐quadratically stable when its stability can be verified by a parameter dependent Lyapunov function. There are already some results in this area. This paper, however, presents less conservative results by adopting more slack‐matrix‐variables in the linear matrix inequalities (LMIs). The parallel distributed compensation (PDC) law is utilized in both the analysis and the synthesis problems. The effectiveness of the new results in this paper is validated by a simulation example. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

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On relaxed LMI-based designs for fuzzy regulators and fuzzy observers

Cited by 34 publications

References 10 publications

Membership-Function-Dependent Stability Analysis and Control Synthesis of Guaranteed Cost Fuzzy-Model-Based Control Systems

Membership-Function-Dependent Stability Analysis and Control Synthesis of Guaranteed Cost Fuzzy-Model-Based Control Systems

Smoothing switched control laws for uncertain nonlinear systems subject to actuator saturation

Poly‐quadratic stability of discrete‐time nonlinear systems in Takagi‐Sugeno's form

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