This paper proposed a novel state estimation framework for nonlinear systems described by fractional-order (FO) and Takagi-Sugeno (TS) fuzzy models, targeting critical challenges associated with large modeling uncertainties. The key innovation was in the development of two complementary observer structures that estimated system states when premise variables were either measurable or non-measurable, and in the presence of unknown inputs and uncertain dynamics. The proposed methodology addressed uncertainties affecting system matrices, input matrices, and unknown input transmission matrices. It introduced a fractional-order Thau-Luenberger observer (FO-TLO) for systems with measurable premise variables, and a dedicated observer adapted to the case of non-measurable premise variables. Both configurations utilized Lyapunov-based stability theory and linear matrix inequality (LMI) methods to ensure robust, asymptotic, and theoretically guaranteed convergence of the state estimation error in the presence of time-varying and bounded uncertainties. The framework extended the observer design to a broader class of FO-TS systems, and it offered effective tools for fault diagnosis, system monitoring, and robust control in the presence of uncertain environments.

This paper presents a scheme of time-delay estimation (TDE) for unknown nonlinear robotic systems with uncertainty and external disturbances that utilizes fractional-order fixed-time sliding mode control (TDEFxFSMC). First, a detailed explanation and design concept of fractional-order fixed-time sliding mode control (FxFSMC) are provided. High performance tracking positions, non-chatter control inputs, and nonsingular fixed-time control are all realized with the FxSMC method. The proposed approach performs better and obtains superior performance when FxSMC is paired with fractional-order control. Furthermore, a TDE scheme is included in the suggested strategy to estimate the unknown nonlinear dynamics. Afterward, the suggested system's capacity to reach stability in fixed time is determined by using Lyapunov analyses. By showing the outcomes of the proposed technique applied to nonlinear robot dynamics, the efficacy of the recommended method is assessed, illustrated, and compared with the existing control scheme.

This paper presents the design of a novel secure communication system based on the dynamics of the Lü hyperchaotic system. In the proposed scheme, the information signal is directly embedded into the hyperchaotic trajectories, ensuring a high level of data concealment. To achieve accurate synchronization between the transmitter and the receiver, a predictive control strategy combined with chaotic modulation is employed. This synchronization mechanism enables precise recovery of the embedded information signal. To evaluate the feasibility and robustness of the proposed cryptosystem, a dual validation framework is adopted. Numerical simulations are carried out using MATLAB/Simulink, and hardware-oriented simulations are performed using Multisim. The strong agreement between the numerical and circuit-level results confirms both the effectiveness and the reliability of the proposed approach. Overall, this work demonstrates the significant potential of hyperchaotic systems for secure communication applications.