Fuzzy observer–based disturbance rejection control for nonlinear fractional-order systems with time-varying delay

Abstract

In this article, a Takagi–Sugeno fuzzy model is applied to deal with the problem of observer-based control design for nonlinear time-delayed systems with fractional-order [Formula: see text]. By applying the Lyapunov–Krasovskii method, a fuzzy observer–based controller is established to stabilize the time-delayed fractional-order Takagi–Sugeno fuzzy model. Also, the problem of disturbance rejection for the addressed systems is studied via the state-feedback method in the form of a parallel distributed compensation approach. Furthermore, sufficient conditions for the existence of state-feedback gains and observer gains are achieved in the terms of linear matrix inequalities. Finally, two numerical examples are simulated for the validation of the presented methods.

Stabilization of delayed fractional‐order T‐S fuzzy systems with input saturations and system uncertainties

“…By introducing a frequency distributed model transformation, a T‐S control technology based on perturbation observer was utilized in Ma and Wang [40], where the stability criterion is obtained by adopting LMIs. According to the state feedback control approach, a disturbance suppression problem for FONSs was solved in Mahmoudabadi and Tavakoli‐Kakhki [41], where a Lyapunov–Krasovskii function is adopted to derive stability conditions. However, the model studied in Ma and Wang [40] does not contain the input saturation function, and in Mahmoudabadi and Tavakoli‐Kakhki [41], the case where the system matrices are unknown is not studied.…”

“…In order to solve this problem, many interesting conclusions have been given, especially emphasizing applications of Lyapunov means, or exploiting some matrix methods to address the impact of time delays, for example, in previous studies [33][34][35][36]. Due to the lack of corresponding stability analysis methods, the stability analysis of FONSs with time delays is very difficult, and only a few relevant results have been reported up to now, for instance, in previous studies [37][38][39][40][41][42]. By using a fuzzy T-S method, positivity and stable performance of time-delay system were investigated in Liu et al [39].…”

“…According to the state feedback control approach, a disturbance suppression problem for FONSs was solved in Mahmoudabadi and Tavakoli-Kakhki [41], where a Lyapunov-Krasovskii function is adopted to derive stability conditions. However, the model studied in Ma and Wang [40] does not contain the input saturation function, and in Mahmoudabadi and Tavakoli-Kakhki [41], the case where the system matrices are unknown is not studied. In addition, it is noted that the above methods are only valid for linearizable FONSs.…”

Time-varying disturbance observer based on sliding-mode observer and double phases fixed-time sliding mode control for a T-S fuzzy micro-electro-mechanical system gyroscope

“…The detail of the sector nonlinearity method for modeling a nonlinear system can be found in Lendek et al, (2011). The application of the T-S fuzzy system can be found in Pavin and Mahsan (2021); Giap et al (2020a); Vafamand (2020); Giap et al (2021a); and Giap et al (2020b). The state and disturbance observers design for a T-S fuzzy will be easier more than these techniques for the nonlinear model.…”

Fuzzy model-based disturbance rejection control for atomic force microscopy with input constraint

“…In this paper, this problem is solved by employing the T-S fuzzy model in order to deal with these difficulties. The T-S fuzzy model is an effective way to represent complex nonaffine nonlinear systems Tsai (2013); Mahmoudabadi and Tavakoli-Kakhki (2021a). The T-S fuzzy model describes the nonlinear systems by a weighted sum of linear subsystems, and every rule of the fuzzy concept is related to one of these linear subsystems.…”