In recent years, fractional order systems and fractional order control have increasingly attracted the attention of researchers in various fields of science and engineering. On the other hand, numerous control approaches have been extended in order to be utilized in fra More
In recent years, fractional order systems and fractional order control have increasingly attracted the attention of researchers in various fields of science and engineering. On the other hand, numerous control approaches have been extended in order to be utilized in fractional order systems. Despite this fact, few research studies have been devoted to generalizing integer order observers to fractional order ones. Since the applications of fractional order systems are increasing, developing fractional order observers seems to be essential. In this paper the problem of non-fragile adaptive sliding mode observer design for a class of fractional-order nonlinear systems with time delay is addressed. First, the states of the fractional-order pseudo-linear time-delay system with matched nonlinearity are estimated employing the sliding mode control method. Then the state estimation problem of fractional order systems with mismatched nonlinearity has been investigated. The asymptotic stability of the estimation error dynamics is proven by employing the Lyapunov stability analysis method for fractional order systems. The sufficient stability conditions are derived in the form of Linear Matrix Inequalities (LMIs). Eventually, the effective performance of the proposed approach in this paper has been corroborated through simulation of a numerical example and also a case study of a fractional order economic system.
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