On relaxed LMI-based design for fuzzy controllers

Teixeira, Marcelo Carvalho Minhoto; Assunção, Edvaldo; Avellar, R.G.

doi:10.1109/fuzz.2001.1009052

Cited by 6 publications

(3 citation statements)

References 13 publications

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“…The main reason is that this method does not apply an accurate model but uses a rule‐based model set instead. A large amount of stability results have been found in the literature by applying the common quadratic Lyapunov function 1–5. Usually, the parallel distributed compensation (PDC) law 6 is utilized.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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

Ding

2009

Asian Journal of Control

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“…For the solution of this problem, in this section sufficient Linear Matrix Inequalities (LMI) conditions for asymptotic stability of linear uncertain systems using state-derivative feedback are presented. The LMI formulation has emerged recently (Boyd et al, 1994) as an useful tool for solving a great number of practical control problems such as model reduction, design of linear, nonlinear, uncertain and delayed systems (Boyd et al, 1994;Assunção & Peres, 1999;Teixeira et al, 2001;Teixeira et al, 2002;Teixeira et al, 2003;Palhares et al, 2003;Teixeira et al, 2005;Assunção et al, 2007a;Assunção et al, 2007b;Teixeira et al, 2006). The main features of this formulation are that different kinds of design specifications and constraints that can be described by LMI, and once formulated in terms of LMI, the control problem, when it presents a solution, can be efficiently solved by convex optimization algorithms (Nesterov & Nemirovsky, 1994;Boyd et al, 1994;Gahinet et al, 1995;Sturm, 1999).…”

Section: Lmi-based Control Design For State-derivative Feedbackmentioning

confidence: 99%

Control Designs for Linear Systems Using State-Derivative Feedback

Cardim¹,

Teixeira²,

Assunção³

et al. 2008

Systems Structure and Control

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“…Ainda pode-se verificar a alocação dos zeros em redução de modelos (Hauksdóttir, 2000), na robustez de sistemas de controle (Tu and Lin, 1992), no controle de vibração (Lee et al, 1987) entre outros temas. A formulação de projetos de sistemas de controle em termos de LMIs (Boyd et al, 1994), tem sido uma ferramenta útil para resolver um grande número de problemas (Assunção and Peres, 1999), (Teixeira et al, 2001), (Teixeira et al, 2003), (da Silva et al, 2004), (Palhares et al, 2003), (Teixeira et al, 2002), (Teixeira and Zak, 1999). As características principais das LMIs são que uma diversidade de especificações e restrições de projeto podem ser descritas na forma de LMIs, e uma vez formulado em termos de LMIs, o problema, quando existe uma solução, pode ser exatamente e eficientemente resolvido com o emprego de algoritmos de otimização convexa (Boyd et al, 1994), (Nesterov and Nemirovsky, 1994).…”

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Alocação de zeros aplicada a sistemas de controle via LMI

Assunção

Andrea

Teixeira

2007

Sba Controle & Automação

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Neste trabalho propõe-se um novo procedimento sistemático de alocação de zeros aplicado em sistemas de controle. Considera-se um sistema de controle com posicionamento de pólos utilizando-se realimentação de estados através de um controlador com matriz de ganhos K. Para realimentar a saída, projeta-se uma matriz de ganhos L do estimador. É proposta uma nova metodologia de alocação de zeros via inequações matriciais lineares (LMIs) para posicionar os zeros dentro de uma região de maneira a diminuir o efeito dos pólos indesejáveis, e ainda para alterar a constante de erro de velocidade do sistema. O uso de LMI para o posicionamento de zeros em uma região é inédito. Exemplos numéricos ilustram a eficiência da metodologia proposta.
A systematic procedure of zero placement to design control systems is proposed. A state feedback controller with vector gain K is used to perform the pole placement. An estimator with vector gain L is also designed for output feedback control. A new systematic method of zero assignment to reduce the effect of the undesirable poles of the plant and also to increase the velocity error constant is presented. The methodology places the zeros in a specific region and it is based on Linear Matrix Inequalities (LMIs) framework, which is a new approach to solve this problem. Three examples illustrate the effectiveness of the proposed method

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On relaxed LMI-based design for fuzzy controllers

Cited by 6 publications

References 13 publications

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

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

Control Designs for Linear Systems Using State-Derivative Feedback

Alocação de zeros aplicada a sistemas de controle via LMI

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