LMI conditions for local stability and stabilization of continuous-time T-S fuzzy systems

Abstract

In this paper, we propose linear matrix inequality (LMI) formulations to analyze local stability and design controllers that locally stabilize continuous-time nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy systems. In order to estimate the domain of attraction (DA), the so-called fuzzy Lyapunov function is used to characterize the subsets of the DA as sublevel sets of the Lyapunov function. Quadratic bounds on the time-derivative of the membership functions are employed to derive the main results. Finally, examples are given to illustrate the proposed methods.

On local H∞ switched controller design for uncertain T–S fuzzy systems subject to actuator saturation with unknown membership functions

“…Based on [26], considering a positive slack variable ϕ and a positive constant 0 , the local H ∞ control problem consists in determining a control law that satisfies the following statements: 1. for w(t) = 0, t ≥ 0, the zero equilibrium point of (9) and (14) is locally asymptotically stable and the ellipsoid…”

“…A good performance of the controlled system can be prejudiced due to the inaccurate representation of the nonlinear system, because usually the operation region and practical constraints, inherent to the plants or actuators, are neglect in the control designs [23]. Thus, several papers have proposed methods that ensure that the state trajectories remain within the operation region in which the fuzzy model T-S is valid [24][25][26] and in [23,[27][28][29] are also considered that the actuator is subject to saturation.…”

“…The design conditions ensure that the closed-loop system, subject to energy-bounded disturbance, has an H ∞ performance, but there is no assurance that the state trajectories will remain within the operation region. In [26], for a known nonlinear system with disturbance bounded by magnitude and energy, the proposed H ∞ fuzzy control guarantees an H ∞ performance and ensures that the state trajectories will not escape from the operation region.…”

“…Additionally, the proposed method is applied in two examples. The first example shows a comparison between the proposed switched control design and the method presented in [26]. The results make it clear that for an uncertain nonlinear system, subject to disturbances with large magnitude, the proposed procedure is the best option.…”

A Takagi-Sugeno fuzzy control of induction motor drive: experimental results

“…The equivalent fuzzy model describes the dynamic behaviour of the system (Tanaka and Sugeno, 1985). This approach has been successfully integrated in nonlinear system modelling and control (Jeung and Lee, 2014;Lee et al, 2015;Tseng et al, 2001).…”