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In this paper, a fractional-order robust adaptive intelligent controller (FRAIC) is designed for a class of chaotic fractional order systems with uncertainty, external disturbances and unknown time-varying input time delay. The time delay is considered both constant and time varying. Due to changes in the equilibrium point, adaptive control is used to update the system's momentary information and the intelligent controller is used to estimate the uncertainties and disturbances and non-linearities of the system according to the momentary information obtained. The sliding mode control, which provides closed loop asymptotic stability in the system despite the uncertainties and disturbances, is used as a robust controller. Using the Lyapunov theorem and Barbalat's Lemma, the asymptotic stability of a chaotic fractional order system with input delay and uncertainty as well as external disturbance is proved by designed controller. Finally, using the simulation results of financial as well as supply and demand systems, the performance of designed controller would be examined.

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In this paper, the problem of robust stabilization of uncertain and perturbed switched nonlinear systems has been investigated. It’s well-known that the solution of H_∞ control problem may not exist for switched systems with a common storage function for all subsystems. On the other hand, by adopting multiple storage functions, different Hamilton-Jacobin inequalities need to be solved. Hence, the robust control problem is addressed here based on passivity, in two cases. First, it is assumed that there is at least one passive subsystem in the whole state space, and the problem is solved based on the average dwell time approach. In this case, by defining the concept of system passivity rate, the admissible range of average dwell time is obtained. In the second case, none of subsystems is passive and the H_∞ control problem is solved by using the feedback passification. In addition to theoretical analysis of the design algorithms, the performance of the theorems for uncertain switched nonlinear systems has been investigated by providing two simulation examples and numerical analysis.