Sufficient condition for stabilization of linear time invariant fractional order switched systems and variable structure control stabilizers

ISA Transactions

Volumn 51, Issue 1, 2012, Pages 65-73

  Balochian, Saeed ^a   Sedigh, Ali Khaki ^b  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b K N TOOSI UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Fractional order switched system; Linear matrix inequality (LMI); Variable structure control

Indexed keywords

CONTROL THEORY; DELAY CONTROL SYSTEMS; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; STABILIZATION;

EXTREMUM SEEKING CONTROL; FRACTIONAL ORDER; FRACTIONAL ORDER SWITCHED SYSTEMS; LINEAR TIME INVARIANT; QUADRATIC FUNCTION; SINGLE LYAPUNOV FUNCTION; STABILIZATION PROBLEMS; SWITCHING CONTROL;

VARIABLE STRUCTURE CONTROL;

ALGORITHM; ARTICLE; COMPUTER SIMULATION; FUZZY LOGIC; INDUSTRY; INSTRUMENTATION; NONLINEAR SYSTEM; STATISTICAL MODEL;

ALGORITHMS; COMPUTER SIMULATION; FUZZY LOGIC; INDUSTRY; LINEAR MODELS; MODELS, STATISTICAL; NONLINEAR DYNAMICS;

EID: 83555164758     PISSN: 00190578     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.isatra.2011.07.010     Document Type: Article

References (41)

1. D. Liberzon Switching in systems and control 2003 Birkhuser Boston (MA)
2. A.S. Morse Control using logic-based switching 1997 Springer Heidelberg (Germany)
3. D. Persis, R.D. Santis, and A.S. Morse Switched nonlinear systems with state-dependent dwell time Systems Control Lett 50 4 2003 291 302
4. R. Sanfelice, R. Goebel, and A. Teel Invariance principles for hybrid systems with connections to detectability and asymptotic stability IEEE Trans Autom Control 52 12 2007 2282 2297
5. D. Liberzon, and A.S. Morse Basic problems in stability and design of switched systems IEEE Control Syst Mag 19 1999 59 70 (Pubitemid 30505850)
6. G. Zhai Stability and L2 gain analysis of switched symmetric systems D. Liu, P.J. Antsaklis, Stability and control of dynamical systems with applications 2003 Birkhuser Boston
7. G. Zhai, and K. Yasuda Stability analysis for a class of switched systems Trans Soc Instrum Control Eng 36 2000 409 415
8. Wicks MA, Peleties P, DeCarlo RA. Construction of piecewise Lyapunov functions for stabilizing switched systems. In: Proceedings of the 33rd IEEE conference on decision and control. 1994. p. 34927.
9. M.A. Wicks, P. Peleties, and R.A. DeCarlo Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems Eur J Control 4 2 1998 140 147 (Pubitemid 128492691)
10. F. Blanchini Set invariance in control Automatica 35 1999 1747 1767 (Pubitemid 32078089)
11. G.V. Smirnov Introduction to the theory of differential inclusions Graduate studies in mathematics vol. 41 2002 American Mathematical Society Providence (RI)
12. Tingshu Hu, Liqiang Ma, and Zongli Lin Stabilization of switched systems via composite quadratic functions IEEE Trans Automat Control 53 11 2008 2571 2585
13. A. Bemporad, and M. Morari Control of systems integrating logic, dynamics, and constraints Automatica 35 3 1999 407 427
14. Feron E. Quadratic stabilizability of switched systems via state and output feedback. Technical report CICS-P-468. MIT. 1996.
15. D. Baleanu, Z.B. Gven, and J.A.T. Machado New trends in nanotechnology and fractional calculus applications 2010 Springer
16. J. Sabatier, O.P. Agrawal, and J.A.T. Machado Advances in fractional calculus, theoretical developments and applications in physics and engineering 2007 Springer London
17. M.D. Ortigueira An introduction to the fractional continuous-time linear systems: the 21st century systems IEEE Circuits Syst Mag 8 3 2008 19 26
18. O.P. Agrawal A general formulation and solution scheme for fractional optimal control problems Nonlinear Dynam 38 2004 323 337 (Pubitemid 40400624)
19. V. Pommier, J. Sabatier, P. Lanusse, and A. Oustaloup Crone control of a nonlinear hydraulic actuator Control Eng Pract 10 4 2002 391 402 (Pubitemid 34412434)
20. Lurie BJ. Three-parameter tunable tiltintegral-derivative (TID) controller. US Patent US5371670. 1994.
21. λDμ controller design for integer and fractional plants using piecewise orthogonal functions Commun Nonlinear Sci Numer Simul 15 5 2009 1267 1278
22. C. Edwards, and S.K. Spurgeon Sliding mode control theory and applications 1998 Taylor & Francis London
23. K. Furuta, and Y. Pan Variable structure control with sliding sector Automatica 36 2000 211 228 (Pubitemid 30544541)
24. Pan Y, Furuta K. Hybrid control with sliding sector. In: Proceedings of 16th IFAC world congress. 2005.
25. Pan Y, Ozguner U. Sliding mode extremum seeking control for linear quadratic dynamic game. In: Proceedings of the American control conference. vol. 1. 2004. p. 6149.
26. El-Khazali R, Ahmad W, Al-Assaf Y. Sliding mode control of fractional chaotic systems. In: First IFAC workshop on fractional differentiation and its applications. 2004. p. 495500.
27. R. El-Khazali, W. Ahmad, and Y. Al-Assaf Sliding mode control of generalized fractional chaotic systems Internat J Bifur Chaos 16 10 2006 1 13
28. El-Khezali R, Ahmad WH. Variable structure control of fractional time-delay systems. In: Proceedings of the 2nd IFAC workshop on fractional differentiation and its applications. 2006.
29. A. Si-Ammour, S. Djennoune, and M. Bettayeb A sliding mode control for linear fractional systems with input and state delays Commun Nonlinear Sci Numer Simul 14 2009 2310 2318
30. S. Balochian, A.K. Sedigh, and A. Zare Stabilization of multi-input hybrid fractional-order systems with state delay ISA Trans 50 2011 21 27
31. M.S. Tavazoei, and M. Haeri Synchronization of chaotic fractional-order systems via active sliding mode controller Physica A 387 1 2008 57 70 (Pubitemid 350051260)
32. A. Pisano, M.R. Rapai, Z.D. Jelii, and E. Usai Sliding mode control approaches to the robust regulation of linear multivariable fractional-order dynamics Int J Robust Nonlinear Control 2010 10.1002/rnc.1565
33. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and applications of fractional differential equations 2006 Elsevier Amsterdam (Netherlands)
34. Matignon D. Stability result on fractional differential equations with applications to control processing. In: IMACS-SMC proceedings. 1996. p. 9638.
35. H.S. Ahn, and Y.Q. Chen Necessary and sufficient stability condition of fractional-order interval linear systems Automatica 44 11 2008 2985 2988
36. Y. Pan, and U. Ozguner Stability and performancee improvement of extremum seeking control with sliding mode Internat J Control 60 2003 968 985
37. R.N. Banavar Extremum seeking loops with quadratic functions: estimation and control Internat J Control 76 2003 1475 1482
38. N. Heymans, and I. Podlubny Physical interpretation of initial conditions for fractional differential equations with RiemannLiouville fractional derivatives Rheol Acta 45 2006 765 771 (Pubitemid 44027219)
39. C. Li, and G. Peng Chaos in Chen's system with a fractional order Chaos Solitons Fractals 22 2004 443 450
40. M.S. Tavazoei, and M. Haeri A necessary condition for double scroll attractor existence in fractional order systems Phys Lett A 367 12 2007 102 113
41. I. Kheirizad, M.S. Tavazoei, and A.A. Jalali Stability criteria for a class of fractional order systems Nonlinear Dynam 61 2010 153 161