Page 167 - Mathematical Techniques of Fractional Order Systems
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Fractional Order Time-Varying-Delay Systems Chapter | 5 155
2
1.5
1
0.5
0
–0.5
0 1 2 3 4 5
FIGURE 5.4 Evolution of the forced system pseudo-state vector xðtÞ under a stabilizing
control low.
0.5
0
–0.5
–1
–1.5
0 1 2 3 4 5
FIGURE 5.5 Zoom on the part near the origin of the evolution of the unforced system pseudo-
state vector xðtÞ.
conditions, new conditions guaranteeing the existence and the synthesis of
pseudo-state feedback stabilizing controller are deduced. The computed con-
troller law ensures the stabilization of unstable fractional order time-varying
delay systems. Examples with an unstable and stable fractional order time-
varying delay systems are studied to illustrate the effectiveness of the pro-
posed approaches.
REFERENCES
Ahmad, W., El-Khazali, R., Al-Assaf, Y., 2004. Stabilization of generalized fractional order cha-
otic systems using state feedback control. Chaos Solitons Fractals 22, 141 150.
Ahn, H., Chen, Y., Podlubny, I., 2007. Robust stability test of a class of linear time-invariant
interval fractional-order system using Lyapunov inequality. Appl. Math. Comput. 187,
27 34.
