Fractional Parametric Uncertainties Research Articles

Non-Fragile Fault-Tolerant Control Design for Fractional-Order Nonlinear Systems With Distributed Delays and Fractional Parametric Uncertainties

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 <inline-formula> <tex-math notation="LaTeX">$H_{\infty} $ </tex-math></inline-formula> 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.

Robust DistributedH∞Filtering for Nonlinear Systems with Sensor Saturations and Fractional Uncertainties with Digital Simulation

This paper is concerned with the robust distributedH∞filtering problem for nonlinear systems subject to sensor saturations and fractional parameter uncertainties. A sufficient condition is derived for the filtering error system to reach the requiredH∞performance in terms of recursive linear matrix inequality method. An iterative algorithm is then proposed to obtain the filter parameters recursively by solving the corresponding linear matrix inequality. A numerical example is presented to show the effectiveness of the proposed method.