Fuzzy sliding mode control design based on stability margins

Stability analysis of dynamic interval type‐2 fuzzy control systems in frequency domain

“…DF approach is a well-known and practical tool in the frequency domain framework to predict the existence of limit cycle [19]. The stability analysis of FCSs has been successfully discussed based on the limit cycles prediction [24][25][26][27][28][29][30][31][32][33][34]. In these studies, integrating the parameter plane, stability equation, and DF methods provides a systematic procedure to analyze the stability of dynamic FCSs [26], uncertain fuzzy vehicle [27], and fuzzy vehicle lateral [30] control systems.…”

“…Analysis of stability margins is a major concern for nonlinear control systems to test controller design. For example, the computation of GM and PM has been carried out for the nonlinear Takagi-Sugeno-Kang FCSs, dynamic FCSs, Takagi-Sugeno [35] PI FCS (T-S PI FCS), and fuzzy sliding mode control systems in [25,31,33,34], respectively.…”

Classical and Fuzzy Sliding Mode Control for a Nonlinear Aeroelastic System with Unsteady Aerodynamic Model

“…The main advantages of SMC are its simplicity, robustness against parameters' variation, perturbations' rejection, and high accuracy [20]. In the other hand, the SMC unignorable inconvenient is known as the chattering phenomenon that has a negative influence on the system's performances and the associated actuators [21].…”

“…To overcome chattering and ensure a finite-time fast system stabilization, SMC is combined with many other controllers [21][22][23][24][25][26]. Second order SMC was combined with the backstepping technique in [22] by adding a disturbance and uncertainty compensator term in the controller's expression, and a modified high order SMC containing a time continuous function describing nonlinearities was proposed in [23].…”

A Center Manifold Theory-Based Approach to the Stability Analysis of State Feedback Takagi-Sugeno-Kang Fuzzy Control Systems

“…The presented short literature survey indicates, as shown in [26] and [27], that the classical approach based on PDC to stabilize fuzzy control systems and the use LMIs in the stability analysis may introduce computational burden, complexity and coupling of subsystems. Therefore, different approaches to LMI-based ones are justified; such also popular approaches include  Bilinear Matrix Inequalities [28,29],  Popov's hyperstability theory [30][31][32][33],  the limit cycle-based approach [34][35][36],  the circle criterion [37][38][39][40];  the harmonic balance method [31], [41][42][43][44], and,  the center manifold theory [45]. Many of these non-LMI-based approaches work only with Mamdani fuzzy controllers and not with Takagi-Sugeno-Kang ones.…”