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The stability theorem of fractional systems is the basis of controlling fractional nonlinear systems. The theorem of fractional nonlinear systems is proved by a new approach in this paper. The results show that the theorem is applicable not only to the fractional nonlinear autonomous system, but also to the fractional nonlinear nonautonomous system. Several examples are analyzed by the theorem, and simulations are carried out, whose results show the effectiveness of the theorem.
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Keywords:
- fractional system /
- stability theorem /
- nonautonomous /
- autonomous
[1] Podlubny I 1999 Fractional Differential Equations (New York: Academic Press)
[2] Mandelbort B B 1983 The Fractal Geometry of Nature (New York: Freeman)
[3] Chen Y Q, Moore K L 2002 Nonlinear Dyn. 29 191
[4] Catherine B, Jonathan R P 200 Syst. Control Lett. 41 167
[5] Zhang H G, Zhao Y, Yu W, Yang D S 2008 Chin. Phys. B 17 4056
[6] Ning D, Lu J A 2005 Acta Phys. Sin. 54 4590 (in Chinese) [宁娣, 陆君安 2005 54 4590]
[7] Bhalekar S, Daftardar-Gejji V 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3536
[8] Sheu L J, Tam L M, Lao S K, Kang Y, Lin K T, Chen J H, Chen H K 2009 Int. J. Nonlinear Sci. Numer. Simulat. 10 33
[9] Ma T D, Zhang H G, Wang Z L 2007 Acta Phys. Sin. 56 3796 (in Chinese) [马铁东, 张化光, 王智良 2007 56 3796]
[10] Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 1441 (in Chinese) [胡建兵, 韩焱, 赵灵冬 2009 58 1441]
[11] Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 4402 (in Chinese) [胡建兵, 韩焱, 赵灵冬 2009 58 4402]
[12] Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 2235 (in Chinese) [胡建兵, 韩焱, 赵灵冬 2009 58 2235]
[13] Li L X, Peng H P, Luo Q, Yang Y X, Liu Z 2013 Acta Phys. Sin. 62 020502 (in Chinese) [李丽香, 彭海朋, 罗群, 杨义先, 刘喆 2013 62 020502]
[14] Sun N, Zhang H G, Wang Z L 2011 Acta Phys. Sin. 60 050511 (in Chinese) [孙宁, 张化光, 王智良 2011 60 050511]
[15] Zhu J, Ray S, Vemula S K 1992 System Theory, Proceedings The 24th Southeastern Symposium on and The 3rd Annual Symposium on Communications, Signal Processing Expert Systems, and ASIC VLSI Design Greensboro, USA, March 1–3, 1992 p355
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[1] Podlubny I 1999 Fractional Differential Equations (New York: Academic Press)
[2] Mandelbort B B 1983 The Fractal Geometry of Nature (New York: Freeman)
[3] Chen Y Q, Moore K L 2002 Nonlinear Dyn. 29 191
[4] Catherine B, Jonathan R P 200 Syst. Control Lett. 41 167
[5] Zhang H G, Zhao Y, Yu W, Yang D S 2008 Chin. Phys. B 17 4056
[6] Ning D, Lu J A 2005 Acta Phys. Sin. 54 4590 (in Chinese) [宁娣, 陆君安 2005 54 4590]
[7] Bhalekar S, Daftardar-Gejji V 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3536
[8] Sheu L J, Tam L M, Lao S K, Kang Y, Lin K T, Chen J H, Chen H K 2009 Int. J. Nonlinear Sci. Numer. Simulat. 10 33
[9] Ma T D, Zhang H G, Wang Z L 2007 Acta Phys. Sin. 56 3796 (in Chinese) [马铁东, 张化光, 王智良 2007 56 3796]
[10] Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 1441 (in Chinese) [胡建兵, 韩焱, 赵灵冬 2009 58 1441]
[11] Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 4402 (in Chinese) [胡建兵, 韩焱, 赵灵冬 2009 58 4402]
[12] Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 2235 (in Chinese) [胡建兵, 韩焱, 赵灵冬 2009 58 2235]
[13] Li L X, Peng H P, Luo Q, Yang Y X, Liu Z 2013 Acta Phys. Sin. 62 020502 (in Chinese) [李丽香, 彭海朋, 罗群, 杨义先, 刘喆 2013 62 020502]
[14] Sun N, Zhang H G, Wang Z L 2011 Acta Phys. Sin. 60 050511 (in Chinese) [孙宁, 张化光, 王智良 2011 60 050511]
[15] Zhu J, Ray S, Vemula S K 1992 System Theory, Proceedings The 24th Southeastern Symposium on and The 3rd Annual Symposium on Communications, Signal Processing Expert Systems, and ASIC VLSI Design Greensboro, USA, March 1–3, 1992 p355
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