Page 600 - Mathematical Techniques of Fractional Order Systems
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570 Mathematical Techniques of Fractional Order Systems
FIGURE 19.1 Phase portrait of integer order Lorenz Stenflo system: (A) for states x and y,
(B) for states z and w, (C) for states y and z, (D) for states z; w, and x.
19.4.1 Controller Design for Stabilization
For the system (19.17), let z 1 5 x 1 and z 2 5 x 2 2 α 1 , where α 1 is the virtual
controller for the first subsystem. It gives,
q
D z 1 52 ðz 2 1 α 1 Þ 2 ax 1 ð19:18Þ
The Lyapunov function can be chosen as below for the subsystem in
(19.18),
