T-S Fuzzy Methodologies For Synchronization And Stabilization Of Fractional Order Chaotic Systems Via Linear Matrix Inequality

In recent years,the synchronization and stabilization of fractional-order systems have gained immense importance and widespread application across numerous disciplines.From secure communication utilizing chaotic systems to unraveling complex behaviors in real-world phenomena,achieving synchronization and stabilization in fractional-order systems is instrumental in advancing fields such as biology,engineering,finance,and control theory.These efforts not only contribute to enhanced control strategies and secure data transmission but also pave the way for novel control paradigms and technologies that harness the unique dynamics of non-integer-order systems,ensuring robustness,resilience,and improved performance in the face of uncertainties and disturbances.In this regard,in this thesis,to solve the problem of the synchronization and stabilization of fractional-order systems,two independent phases are presented.The first phase,addresses the synchronization and stabilization challenges in fractional-order systems affected by uncertainties,external disturbances,and input saturations.In the first phase,a model-free Takagi-Sugeno(T-S)fuzzy state feedback controller is meticulously designed,leveraging Linear Matrix Inequalities and Lyapunov stability theorem.The approach not only achieves synchronization and stabilization goals but also guarantees cost-effective control,surpassing the performance of existing works.Through comprehensive numerical simulations,the designed controller showcases its superiority in managing the complexities of fractionalorder dynamics,uncertainties,and disturbances.The integration of T-S fuzzy method,linear matrix inequality,and Lyapunov stability theorem results in a robust control strategy that ensures synchronization and stabilization of systems with fractional-order dynamics and input saturations.Moreover,the presented approach’s superiority over existing methods is demonstrated quantitatively through comparative simulations,reaffirming its effectiveness in achieving improved control performance and cost-efficiency.In the second phase of this research,a novel model-free T-S fuzzy sliding mode control strategy is proposed for the synchronization of fractional-order systems.This approach finds application in the realm of image encryption,offering a robust solution to the challenges posed by uncertainties,external disturbances,and input saturations.The synchronization of chaotic fractional-order systems is a crucial component in secure image encryption techniques.The proposed T-S fuzzy sliding mode control controller,integrated with linear matrix inequality and Lyapunov stability theorem,establishes a solid foundation to address the intricacies of fractional-order systems.It achieves synchronization objectives even in the presence of uncertainties and disturbances,while accommodating input saturations.The numerical simulations conducted in this phase reveal the proposed method’s astonishing superiority over existing techniques,not only in terms of synchronization precision but also in encryption security.Through a rigorous comparative analysis against established methods,this paper quantifies the exponential leap in synchronization and security achieved by the model-free TS fuzzy sliding mode control controller.This groundbreaking research redefines the landscape of secure communication,carving a path toward an era of unassailable encryption and chaos control.The application of this control strategy in image encryption involves synchronizing chaotic fractional-order systems to establish secure communication channels.linear matrix inequality and Lyapunov stability theorem provide a mathematical framework to ensure robust synchronization,thereby enhancing the security of the encryption process.The controller’s adaptability to uncertainties,external disturbances,and input saturations significantly improves the resilience of the encryption scheme against potential attacks and system perturbations.The study includes comprehensive analysis,simulation results,and performance evaluation,highlighting the efficiency of the model-free T-S fuzzy sliding mode control controller in achieving synchronization for image encryption.The research showcases the applicability of this approach in enhancing the security and reliability of image encryption systems,thereby contributing to the broader field of secure communication and data protection.Moreover,for a more comprehensive evaluation of the cryptographic protocol’s effectiveness,the paper provides performance and security analyses.These analyses serve to validate the superiority of the proposed encryption scheme and encompass techniques such as histogram analysis,assessment of adjacent pixel correlations,and examination of information entropy.