Stabilizing controller design for uncertain nonlinear systems using fuzzy models

Guaranteed cost fuzzy controllers for a class of uncertain nonlinear dynamic systems

“…linear systems is extended to deal with the T-S fuzzy systems [7]- [10]. In the framework of T-S fuzzy systems, parametric uncertainty can be represented in general by norm-bounded or polytopic uncertain sets.…”

“…for Local uncertain linear models of (2) are constructed by extending the linearization formula proposed by Teixeira and Zak [10], which yields a good approximates of the system in the vicinity of the operating point even if the operating point is not an equilibrium point. The T-S fuzzy system adopted in this work is inferred as a weighted average of local input-output relations of (2) and can be represented byẋ…”

Robust multi-criteria optimal fuzzy control of continuous-time nonlinear systems

“…Based on the T-S fuzzy model framework, many systematic approaches for stability analysis, observer design, and control synthesis are CONTACT Xin Wang xwang@siue.edu studied in the literature. Particularly, the control synthesis based on quadratic Lyapunov function approaches has been extensively studied in Fang, Liu, Kau, Hong, & Lee (2006); Kim & Lee (2000); Liu & Zhang (2003); Sala & Arino (2007); Teixeira & Zak (1999); Teixeira, Assuncao, & Avellar (2003);and Tuan, Apkarian, Narikiyo, & Yamamoto (2001). Since a common quadratic Lyapunov function is independent of fuzzy membership functions, the results based on a single Lyapunov function might be conservative.…”

Realimentação derivativa e modelo fuzzy Takagi-Sugeno para controle da articulação do joelho de pacientes paraplégicos com o uso de acelerômetros

“…There are several FES studies, including different muscle and knee joint mathematical models, regarding the movement control of paraplegic patients. In Gaino (2009) and Teixeira et al (2006a,b), studies and simulations of a paraplegic's leg position control were performed for the first time using Takagi-Sugeno (T-S) fuzzy models (Takagi and Sugeno, 1985;Tanaka et al, 1998;Teixeira and Żak, 1999). The leg mathematical model, proposed by Ferrarin and Pedotti (2000), was adopted to obtain the relationship between the muscle torque with the pulse width of the electrical signal stimulation.…”

“…(Tanaka et al, 1998) and LMIs (Linear Matrix Inequalities) (Gahinet et al, 1995). This method enables the fuzzy combination of the feedback gain matrices, resulting in a fuzzy regulator that can stabilize the whole system (Teixeira and Żak, 1999). The regulator was designed for an operation at 30°, i.e., the leg goes from a resting state and stabilizes at 30°.…”