Condiçoes LMIs alternativas para sistemas Takagi-Sugeno via função de Lyapunov Fuzzy

Mozelli, Leonardo Amaral; Avellar, Gustavo S. C.; Palhares, Reinaldo M.; Santos, Rafael Ferreira dos

doi:10.1590/s0103-17592010000100008

Cited by 2 publications

(2 citation statements)

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“…The modeling, analysis and control of nonlinear systems via linear models are not restricted to approaches based on LDIs. In this sense, Mamdani and Takagi Sugeno fuzzy systems play also an important role (Montagner et al, 2010;Mozelli et al, 2010;Tognetti and Oliveira, 2010). These type of fuzzy systems allow nonlinear systems to be approximated by means of an averaged sum of linear models.…”

Section: Introductionmentioning

confidence: 99%

“…These type of fuzzy systems allow nonlinear systems to be approximated by means of an averaged sum of linear models. Then, the problems of analysis and synthesis can be written in terms of LMIs (Montagner et al, 2010;Mozelli et al, 2010). Also, based on feedback linearization technique, adaptative neural networks or fuzzy control schemes have been introduced to approximate nonlinear systems into linear models (Chen et al, 1996).…”

Section: Introductionmentioning

confidence: 99%

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A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

Kuiava

Ramos

Pota

2012

Sba Controle & Automação

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A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%