The Takagi–Sugeno (T–S) fuzzy model is a versatile approach widely used in system control, often in combination with other strategies. This paper addresses key control challenges linked to the T–S system and presents important considerations to ensure its successful application using the Lyapunov theorem. One crucial aspect is determining the optimal number of premise variables and selecting accurate fuzzy rules for the T–S model. Additionally, the theorem based on Linear Matrix Inequality (LMI) is developed to enable effective disturbance rejection. To enhance stability control, constraints are imposed on the output angle and control input of a rotary inverted pendulum (RIP). By integrating T–S fuzzy control, disturbance rejection, and input/output constraints, robust stability in controlling the RIP is achieved. Extensive simulations are performed to showcase the efficiency of the suggested method, and the simulation results are thoroughly discussed and analyzed to verify the efficacy of the control method.

Precise control of overhead crane systems, especially when there are disturbances, is crucial for ensuring safety and efficiency in operations. This paper addresses tracking control for overhead cranes that have variable cable lengths. It employs the Takagi-Sugeno (T-S) descriptor fuzzy method combined with Input Shaping (IS) techniques to significantly reduce payload oscillation. By representing the nonlinear system as local linear sub-models over different operating regions, the T-S descriptor fuzzy method effectively controls the crane system’s high nonlinearity. The Parallel Distributed Compensation (PDC) Integral controller is integrated into the design framework to enhance tracking control performance. Using Lyapunov theory, linear matrix inequalities (LMIs) are constructed, and the controller parameters are determined by solving these inequalities. By incorporating H-infinity or L-infinity performance criterion into the fuzzy model, robust controllers are developed to effectively reject disturbances and ensure tracking performance. Finally, simulations are conducted to evaluate the performance and effectiveness of the proposed controllers.

Research on combined control methods for quadrotors has focused on trajectory tracking, robust control, neural networks, parameter optimization, and path planning. While previous studies have not fully integrated all of these aspects, this study presents a comprehensive control framework that seamlessly combines robust control strategies, neural network-based uncertainty approximation, path planning, and optimization to achieve precise and reliable trajectory tracking of quadrotors operating under significant model uncertainties and external disturbances. At the heart of the framework is the Integrated sliding mode control (Intergrated SMC), a design that merges the inherent robustness of sliding mode control with the adaptive approximation capability of radial basis function (RBF) neural networks. The fusion of these two elements not only ensures stability but also strengthens the system’s resilience, delivering high-precision tracking even in the presence of unmodeled dynamics and external disturbances. The framework also incorporates the rapidly-exploring random tree star (RRT*) algorithm for trajectory planning, allowing the generation of collision-free and asymptotically optimal reference paths capable of navigating environments with complex obstacle distributions. In addition, particle swarm optimization (PSO) is employed to systematically tune the controller gains and neural network parameters, thereby enhancing overall control performance. Extensive simulations under varying conditions of model mismatch and disturbances confirm the superior performance of the proposed integrated approach, demonstrating significant improvements in tracking accuracy and disturbance rejection compared to conventional control methods. This unified architecture thus provides a robust and computationally efficient solution for quadrotor trajectory tracking, maintaining high performance even in the presence of model uncertainties and external disturbances.