Controller Design for Discrete-Time Descriptor Models: A Systematic LMI Approach

Estrada-Manzo, Víctor; Lendek, Zsófia; Guerra, Thierry Marie; Pudlo, Philippe

doi:10.1109/tfuzz.2014.2371029

Cited by 32 publications

(16 citation statements)

References 37 publications

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“…Based on the definition of multiple sum in [23], the following definitions can be formulated, see [23] for further details.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…Remark 5: Based on the definition of multiple sums in [23], Corollary 1 provides a general framework of the conditions with multiple sums for T-S fuzzy descriptor systems (4) contain, the less conservative the conditions will be, but at the same time, the more decision variables and LMIs will be involved. For the design purpose, only one sum in w i , i = 1, 2, · · · , rr e , is considered.…”

Section: Using the Schur Complement (20) Holds If And Only If The Fomentioning

confidence: 99%

“…Therefore, if (23) can be guaranteed by the LMIs in (32), then the asymptotic stability of the ideal sliding mode dynamics (14) will be proved.…”

Section: Using the Schur Complement (20) Holds If And Only If The Fomentioning

confidence: 99%

“…The advantages of the T-S fuzzy descriptor model are a reduction in the number of fuzzy rules and a tighter nonlinear system representation [14]. Over recent years, a great deal of effort has been devoted to the study of T-S fuzzy descriptor systems and many significant results have been achieved in diverse areas, for example, stability and stabilization [15]- [23], observer-based control [24]- [25], guaranteed cost control [26]- [27], H ∞ and dissipative control [28]- [31], and fault-tolerant control [32].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, the first motivation is to study sliding mode control problems for mechanical systems in descriptor form. Mechanical systems are always described by T-S fuzzy descriptor systems where the derivative-term coefficients are different for each local subsystem [23]. In this case, the sliding mode control methods in [19], [31] for T-S fuzzy descriptor systems that share the same derivative-term coefficient for each local subsystem can not be directly applied.…”

Section: Introductionmentioning

confidence: 99%

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Observer-Based Fuzzy Integral Sliding Mode Control For Nonlinear Descriptor Systems

Zhang

Yan

et al. 2018

IEEE Trans. Fuzzy Syst.

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Abstract-This paper investigates observer-based stabilization for nonlinear descriptor systems using a fuzzy integral sliding mode control approach. Observer-based integral sliding mode control strategies for the T-S fuzzy descriptor systems are developed. A two step design is first developed to obtain the observer gains and coefficients in the switching function using linear matrix inequalities, and the results are used to facilitate the development of a single step design approach, which is seen to be convenient but introduces some conservatism in the design. The potential application to a class of mechanical systems is also considered. Since the descriptor system representation of mechanical systems is adopted, it is shown that in contrast to the existing fuzzy sliding mode control methods based on the normal system representation, the resulting T-S fuzzy system does not contain different input matrices for each local subsystem and the required number of fuzzy rules is consequently markedly reduced. Finally, the balancing problem of a pendulum on a car is numerically simulated to demonstrate the effectiveness of the proposed method.Index Terms-Observer-based stabilization, T-S fuzzy descriptor systems, integral sliding mode control, mechanical systems.

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“…Based on the definition of multiple sum in [23], the following definitions can be formulated, see [23] for further details.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Section: Using the Schur Complement (20) Holds If And Only If The Fomentioning

confidence: 99%

“…Therefore, if (23) can be guaranteed by the LMIs in (32), then the asymptotic stability of the ideal sliding mode dynamics (14) will be proved.…”

Section: Using the Schur Complement (20) Holds If And Only If The Fomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Observer-Based Fuzzy Integral Sliding Mode Control For Nonlinear Descriptor Systems

Zhang

Yan

et al. 2018

IEEE Trans. Fuzzy Syst.

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Discrete reference tracking control to swing up an electric wheelchair

Gray

Guerra

Delprat

et al. 2023

Asian Journal of Control

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Mobility using wheelchair is a crucial feature for disabled people. Between a manual wheelchair and an electric wheelchair, there is a very interesting and promising solution consisting of an electrical kit that converts a manual wheelchair to an electric wheelchair. Autonomad‐Mobility is a company selling such kits, where the wheels are equipped with a brushless motor. It presents new possibilities for mobility, especially for crossing obstacles and running on different types of soil. Several methods have been tested, from linear to nonlinear ones including the linear parameter‐varying control framework. Nevertheless, the most dangerous and critical issue is to be able to produce a so‐called safe and robust swing‐up: the transition from standard mode (four wheels on the ground) to gyroscopic mode (the wheelchair balancing on the rear push‐wheels). The gyroscopic mode is a unique feature improving mobility by providing a way to overcome obstacles that would normally be unsurpassable due to the caster wheels. Whereas some results exist, the solution must be compatible with any wheelchair and any disabled person whatever is her/his height and weight. Robustness of this unstable feature is therefore the key point of the work knowing that “exact” modeling is unrealistic. With the model in descriptor form and using the quasi‐linear parameter‐varying framework new stabilization conditions formulated as linear matrix inequality constraints are developed for attaining the goal. Simulations and real‐time experiments demonstrate the interest of this approach.

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