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This paper discusses the stability issues of fractional-order nonlinear scalar systems by using the distributed-order operators and the order sensitivity method. A positivity check method is proposed by the use of initialized fractional calculus. By doing so, the fractional-order system is converted to a corresponding distributed-order one, and a group of Lyapunov function candidates of the distributed-order...
The fractional-order Hammerstein system is a cascading system composed of a static nonlinearity followed by a fractional-order linear dynamics, which is a typical nonlinear system satisfying the local Lipschitz condition, and exhibits quasi-linear properties. This paper combines the fractional-order iterative learning control (FOILC) and the fractional-order iterative learning identification (FOILI),...
In this paper, we discuss in time domain the convergence of the iterative process for fractional-order nonlinear systems. A linear adaptive generalized fractional-order iterative learning control scheme is derived, which guarantees the convergence of the algorithm without the knowledge of the system order. The implementation of generalized fractional-order iterative learning controllers can be achieved...
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