MIMO Systems Properties Preservation Under SPR Substitutions

IEEE Transactions on Circuits and Systems II: Express Briefs

Volumn 51, Issue 5, 2004, Pages 222-227

  Fernandez Anaya, G ^a   Martinez Garcia, J C ^b   Kucera, V ^c   Aguilar George, D ^b  

^a INSTITUTO MEXICANO DEL PETRÓLEO   (Mexico)

^b DEPARTAMENTO DE FÍSICA   (Mexico)

^c CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

Author keywords

Continuous linear time invariant multi input multi output (MIMO) systems; control oriented properties; properties preservation; stability; strictly positive real (SPR) functions; substitutions; unforced systems

Indexed keywords

CONTROL SYSTEM ANALYSIS; LAPLACE TRANSFORMS; LINEAR CONTROL SYSTEMS; MATHEMATICAL MODELS; SYSTEM STABILITY; TRANSFER FUNCTIONS;

CONTROL-ORIENTED PROPERTIES; MULTIPLE INPUT MULTIPLE OUTPUT SYSTEMS; PROPERTIES PRESERVATION; STRICTLY POSITIVE REAL FUNCTIONS;

TIME VARYING CONTROL SYSTEMS;

EID: 2942568429     PISSN: 15497747     EISSN: 15583791     Source Type: Journal    
DOI: 10.1109/TCSII.2004.824050     Document Type: Article

References (23)

1. B.D.O. Anderson and S. Vongpanitlerd, Network Analysis and Synthesis. A Modern Systems Approach. Englewood Cliffs, NJ: Prentice-Hall, 1972.
2. F.J. D'Amato, M.A. Rotea, A.V. Megretzki, and U.T. Jönsson, “New results for analysis of systems with repeated nonlinearities,” Automatica, vol. 37, pp. 739-747, 2001.
3. C.A. Desoer and M. Vidyasagar, Feedback Systems Input-Output Properties. New York: Academic, 1975.
4. nl analysis: applications to nonlinear PI controlers,” in Proc. IEEE Conf. on Decision and Control, Dec. 2002, pp. 2480-2485.
5. G.C. Goodwin and K.S. Sin, Adaptive Filtering, Prediction and Control. Englewood-Cliffs, NJ: Prentice-Hall, 1984.
6. G. Fernández, “Preservation of SPR functions and stabilization by substitutions in SISO plants,” IEEE Trans. Automat. Contr., vol. 44, pp. 2171-2174, Nov. 1999.
7. ∞-robustness preservation in SISO systems when applying SPR substitutions,” Int. J. Contr., vol. 76, no. 7, pp. 728-740, 2003.
8. W.M. Haddad and D.S. Bernstein, “Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to Robust stability part I: Continuous-time theory,” Int. J. Robust Nonlinear Contr., vol. 3, pp. 313-339, 1993.
9. C.H. Huang, P.A. Ioannou, J. Maroulas, and M.G. Safonov, “Design os strictly positive real systems using constant output feedback,” IEEE Trans. Automat. Contr., vol. 44, pp. 569-573, Mar. 1999.
10. P.A. Ioannou and J. Sun, Robust Adaptive Control. Upper Saddle River, NJ: Prentice-Hall, 1995.
11. H.K. Khalil, Nonlinear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1996.
12. V.V. Kulkarni and M.G. Safanov, “All multipliers for repeated monotone nonlinearities,” IEEE Trans. Automat. Contr., vol. 47, pp. 1209-1212, June 2002.
13. R. Lozano, B. Brogliato, B. Maschke, and O. Egeland, Dissipative Systems Analysis and Control: Theory and Applications. London, U.K.: Springer-Verlag, 2000.
14. R. Mancera and M.G. Safanov, “An algorithm to compute multipliers for repeated monotone nonlinearities,” in Proc. IEEE Conf. on Decision and Control, Dec. 2002, pp. 4162-4166.
15. K.S. Narendra and A.M. Annaswamy, Stable Adaptive Systems. Englewood Cliffs, NJ: Prentice-Hall, 1989.
16. K.S. Narendra and J.H. Taylor, Frequency Domain Criteria for Absolute Stability. New York: Academic, 1973.
17. B.T. Polyak and Y.Z. Ya. Z. Tsypkin, “Stability and robust stability of uniform systems,” Automat. Remote Contr., vol. 57, pp. 1606-1617, 1996.
18. M.G. Safonov, E.A. Jonckheere, M. Verma, and D.J. Limebeer, “Synthesis of positive real multivariable feedback systems,” Int. J. Contr., vol. 45, no. 3, pp. 817-842, 1987.
19. M.G. Safanov and V.V. Kulkarni, “Zames-Falb multipliers for MIMO nonlinearities,” Int. J. Robust Nonlinear Control, vol. 10, pp. 1025-1038, 2000.
20. W. Sun, P.P. Khargonekar, and D. Shim, “Solution to the positive real control problem for linear time-invariant systems,” IEEE Trans. Automat. Contr., vol. 39, pp. 2034-2046, Nov. 1994.
21. 2-Gain and Passivity Techniques in Nonlinear Control. New York: Springer-Verlag, 1996.
22. L. Wang, “Robust performance of a class of control systems,” Institute for Mathematics and Its Applications, Essex, U.K., Preprint series, no. 1842, Feb. 2002.
23. G. Zames and P. Falb, “Stability conditions for systems with monotone and slope-restricted nonlinearities,” SIAM J. Control Optimiz., vol. 6, pp. 89-108, 1968.