Stabilization of nonlinear fractional order faulty systems with time-varying delay

Abstract

This paper focuses on the issue of stabilization of nonlinear fractional order time-delay systems in the presence of fault. A general class of nonlinear fractional order systems is considered in which fault causes variations in the system dynamic and actuators. Besides, time-varying delay is noticed in the system equations that is of high importance in control of real-life systems. In order to facilitate the problem of controller design for such systems, a precise method for modeling complex nonlinear systems, namely, Takagi–Sugeno fuzzy model, is adopted. Regarding a Caputo derivative–based Lyapunov–Krasovskii functional, new delay-dependent stabilization conditions are established in the form of linear matrix inequalities. Eventually, two examples including a truck–trailer and Lorenz system are simulated in order to evaluate the results of this research work.