This work discuss the stabilization issue for a class of fractional-order nonlinear systems together with time delay, parametric uncertainties and actuator faults. Precisely, the considered system comprises of two delays namely distributed delay and time-varying delay. Moreover, the occurrence of the actuator faults and fractional parametric uncertainties may induce poor performance of the systems. To overcome these issue, a non-fragile fault-tolerant controller is designed which makes the system asymptotically stable with the specified mixed H ∞ and passive performance index. A fractional Razumikhin theorem is applied to handle the distributed delay term in the stabilization analysis. With the aid of suitable Lyapunov-Krasovskii functional, the sufficient conditions are established in terms of linear matrix inequalities together with Razumikhin stability theorem for getting the required results. By virtue of this, the controller gain matrix is obtained by solving the obtained LMIs and the graphical results are simulated using FOMCON toolbox. Later, the potency of the developed results are validated by virtue of three numerical examples including a rocket motor chamber.INDEX TERMS Fractional-order nonlinear systems; Distributed delay; Reliable controller; Gain perturbation; Fractional uncertainties; Mixed H ∞ and passive performance.
This article focuses on the concerns of a tracking control and active disturbance rejection for nonlinear switched systems described by Takagi–Sugeno fuzzy framework with state‐dependent nonlinear perturbations, actuator saturations and disturbances. Especially, a nonlinear equivalent‐input‐disturbance technique is employed to guarantee that only the external disturbances are rejected while retaining the beneficial nonlinearity of the system. Notably, with the aid of the lifting technique, the modified repetitive control are accurately described by a continuous‐discrete two‐dimensional model is designed to improve the tracking precision. The fuzzy‐membership‐function‐dependent piecewise Lyapunov–Krasovskii functional (LKF) by exploiting the knowledge of the membership functions are built to assure the exponential stability of the investigated system. Moreover, the controller and observer gains can be obtained as solutions to a set of strict linear matrix inequalities. Finally, an application example based on the cognitive radio model is given to verify the efficacy of the proposed control protocol.
This study emphasis on the problem of state tracking and disturbance attenuation for Takagi-Sugeno fuzzy based model with input time-delay via improved extended state observer based predictive proportional-integral tracking control.To be precise, a predictive proportional-integral tracking controller is formulated by implementing the Smith-Predictor strategy to restrain the influence of input time-delay. Then, with the aid of improved extended state observer, the lumped disturbance is estimated and it is combined with the predictive proportional-integral tracking control for disturbance attenuation. Further, closed-loop control-system is considered to ensure the satisfactory state tracking results for the considered system regardless of time-delay in the control input and lumped disturbances. Meanwhile, based on the Lyapunov theory approach, the stability criteria for the proposed system are formulated in terms of linear matrix inequalities following which the gain matrices are derived. Finally, in order to evident the supremacy of the proffered control system, two numerical simulation results are provided.
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