A non-quadratic Lyapunov functional for H∞ control of nonlinear systems via Takagi–Sugeno models

Marquez, Raymundo; Guerra, Thierry Marie; Bernal, Miguel; Kruszewski, Alexandre

doi:10.1016/j.jfranklin.2016.01.004

Cited by 57 publications

(41 citation statements)

References 46 publications

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“…As is readily seen, the observer (7) and (8) reduces to the PDO if P j = P, j = 1, · · · , r. Multiple Lyapunov matrices P j , j = 1, · · · , r obviously allow a wider region of solutions of the observer design conditions (10)- (13). The observer (7) and (8) and its multiple Lyapunov function also adopt the integral of the membership function, as well as its time delay function, which help (1) reduce the conservatism in the observer design conditions (10)- (13) and (2) avoid the derivatives of the membership functions in the observer design [17,18]. The knowledge of the derivative of the membership function is a tight requirement because the membership functions are not always differentiable and may not be calculated in advance.…”

Section: Calculate Gain Matrices (14)-(18)mentioning

confidence: 99%

“…Theorem 1 adopts Lemma 1 for the relaxation of its design condition. It is known [17] that although more decision variables are needed, Lemma 2 can make further relaxation of the conditions of Theorem 1. In fact, it follows from Lemma 2 and (30) that the condition (12) in Theorem 1 can be replaced by:…”

Section: Calculate Gain Matrices (14)-(18)mentioning

confidence: 99%

“…The membership functions are not always differentiable, and their upper bounds are not easily calculated in advance. The recent papers [17,18] proposed the control design method based on a new multiple Lyapunov function approach. Since their Lyapunov function has an integral of the membership functions, any information on the derivatives of the membership functions is not necessary.…”

Section: Introductionmentioning

confidence: 99%

“…In these cases, this design method is infeasible. Followed by [17,18], a class of multiple Lyapunov functions that contain an integral of the membership function of fuzzy systems is adopted. This approach requires no information on the derivative of the membership function and is shown to reduce the conservatism in control design conditions.…”

Section: Introductionmentioning

confidence: 99%

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A New Observer Design for Fuzzy Bilinear Systems with Unknown Inputs

Yoneyama

2017

Designs

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An observer design for a class of nonlinear systems with unknown inputs is considered. Takagi-Sugeno fuzzy bilinear systems represent a wide class of nonlinear systems, and these systems with unknown inputs are an ideal model for many physical systems. For such systems, a design method for obtaining an observer that estimates the state of the system is proposed. A parallel distributed observer (PDO), which is constructed with local linear observers and the appropriate grade of the membership functions, is a conventional observer for Takagi-Sugeno fuzzy bilinear systems. However, it is known that its design conditions have conservativeness. In this paper, to reduce the conservatism in the design conditions, non-PDO with new design conditions is proposed. Our design conditions are derived from a multiple Lyapunov function, which depends on the membership function with time-delay in the premise variables. This method eventually reduces the conservatism and enables us to construct an observer for a wide class of nonlinear systems. When the premise variables are the state variables that are not measurable, Takagi-Sugeno fuzzy bilinear systems can represent a wider class of nonlinear systems. Hence, an observer design for fuzzy bilinear systems with unmeasurable premise variables is also proposed. Finally, numerical examples are given to illustrate our design methods.

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Section: Calculate Gain Matrices (14)-(18)mentioning

confidence: 99%

Section: Calculate Gain Matrices (14)-(18)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A New Observer Design for Fuzzy Bilinear Systems with Unknown Inputs

Yoneyama

2017

Designs

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“…System modeling is the first step which constructs a fuzzy model such as T-S fuzzy model or polynomial fuzzy model to describe the dynamics of the nonlinear plant and capture its characteristic. Depending on the nature of the nonlinear plant, variations of T-S fuzzy model/polynomial fuzzy model can be employed to capture the characteristic, just to a name a few, such as disturbance [114,88,115,116], input nonlinearity/saturation [117,85,118,119,120], jumping [121], positivity [122,123,124,125,69], stochastic processes [126,127], time delay [128,129,130], switching [131,79,132,133,134], uncertainties [46,135,87], etc., in continuous-time/discrete-time form.…”

Section: Introductionmentioning

confidence: 99%

A review on stability analysis of continuous-time fuzzy-model-based control systems: From membership-function-independent to membership-function-dependent analysis

Lam

2018

Engineering Applications of Artificial Intelligence

224

111

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Takagi‐Sugenoexact model and linear matrix inequalities for an active power filter control

González

Pérez

Beristain

2021

Int Trans Electr Energ Syst

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In order to take advantage of the capabilities of a shunt active power filter (SAPF), the design of an adequate control scheme must be developed; generally, the SAPF control scheme corresponds to a cascade control composed of an inner loop and an outer loop. This article approaches the design of an inner loop control based on linear matrix inequalities (LMIs) for a SAPF with LCL coupling filter. The control design begins with the system rewriting in exact Takagi-Sugeno (TS) models, in the sequel, through the use of a quadratic energy function, and considering the closed-loop system, the Lyapunov direct method to establish LMI conditions is used. This proposal of inner loop control is called TSLMI, and in conjunction with a PI control, a PI-TSLMI cascade control scheme is configured. The SAPF objectives are the reduction of the total harmonic distortion (THD) in the mains current, the power factor (PF) correction, and facing load changes. The results show a correct performance of the proposed PI-TSLMI for both simulation and experimental tests.

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A non-quadratic Lyapunov functional for H∞ control of nonlinear systems via Takagi–Sugeno models

Cited by 57 publications

References 46 publications

A New Observer Design for Fuzzy Bilinear Systems with Unknown Inputs

A New Observer Design for Fuzzy Bilinear Systems with Unknown Inputs

A review on stability analysis of continuous-time fuzzy-model-based control systems: From membership-function-independent to membership-function-dependent analysis

Takagi‐Sugenoexact model and linear matrix inequalities for an active power filter control

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