Abstract

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.

Highlights

  • T HE concept of fractional calculus has been demanding considerable attention in recent years

  • The fractional-order (FO) dynamical systems are more accurate than the integer-order systems, the stability and stabilization analysis of FO systems are more intricate than the systems of integer-order

  • It is of utmost importance to consider the nonlinearity in the fractional-order control systems upon studying their stability and stabilization analysis [6]- [10]

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Summary

Introduction

T HE concept of fractional calculus has been demanding considerable attention in recent years. The fractional-order (FO) dynamical systems are more accurate than the integer-order systems, the stability and stabilization analysis of FO systems are more intricate than the systems of integer-order. Despite their complexity, fractional-order systems have acquired significant attention due to their remarkable applications in the field of control engineering and several works have been presented in literature [1]- [5]. In [6], a nonlinear FO system with time-delays is considered and the stability is achieved via LMI-based design through observer-based control problem. The authors in [9] have studied the stability analysis by developing sufficient conditions for FO nonlinear systems with time-varying delay

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