Robust stability bounds of uncertain fractional-order systems
This paper considers the robust stability bound problem of uncertain fractional-order systems. The system considered is subject either to a two-norm bounded uncertainty or to a infinity-norm bounded uncertainty. The robust stability bounds on the uncertainties are derived. The fact that these bounds are not exceeded guarantees that the asymptotical stability of the uncertain fractional-order systems is preserved when the nominal fractional-order systems are already asymptotically stable. Simulation examples are given to demonstrate the effectiveness of the proposed theoretical results.
Key Words and Phrasesfractional-order system linear matrix inequality robust stability bound uncertainty
MSC 2010Primary 26A33 Secondary 34A08, 34D10, 93C73, 93D09, 93D21
Unable to display preview. Download preview PDF.
- Z. Jiao and Y.Q. Chen, Impulse response of a generalized fractional second order filter. Fract. Calc. Appl. Anal. 15, No 1 (2012), 97–116; DOI: 10.2478/s13540-012-0007-2; at http://link.springer.com/article/10.2478/s13540-012-0007-2.MATHMathSciNetGoogle Scholar
- Z. Jiao and Y.Q. Chen, Stability analysis of fractional-order systems with double noncommensurate orders for matrix case. Fract. Calc. Appl. Anal. 14, No 3 (2011), 436–453; DOI: 10.2478/s13540-011-0027-3; at http://link.springer.com/article/10.2478/s13540-011-0027-3.MATHMathSciNetGoogle Scholar
- R.L. Magin, Fractional calculus models of complex dynamics in biological tissues. Computers and Mathematics with Appl. 59, No 5 (2010), 1586–1593.Google Scholar
- D. Matignon, Stability results for fractional differential equations with applications to control processing. In: IMACS, IEEE-SMC Lille, France (1996), 963–968.Google Scholar
- R.R. Nigmatullin, A.A. Arbuzov, F. Salehli, A. Giz, I. Bayrak, and H. Catalgil-Giz, The first experimental confirmation of the fractional kinetics containing the complex-power-law exponents: Dielectric measurements of polymerization reactions. Physica B: Condensed Matter 388, No 1–2 (2007), 418–434.CrossRefGoogle Scholar
- I. Petras, Y.Q. Chen, B.M. Vinagre, and I. Podlubny, Stability of linear time invariant systems with interval fractional orders and interval coefficients. In: Second IEEE Int. Conference on Computation Cybernetics Viena Austria (2005), 341–346.Google Scholar
- J. Sabatier, C. Farges, and J.C. Trigeassou, Fractional systems state space description: some wrong ideas and proposed solutions. J. on Vibration and Control, To appear, DOI: 10.1177/1077546313481839.Google Scholar