STRATEGIC FUNCTIONS FOR FEEDBACK STABILIZATION OF BILINEAR SYSTEMS

M. Ouzahra and R. El Ayadi

References

  1. [1] C. Bruni, G. Dipillo, & G. Koch, Bilinear systems: an appealingclass of nearly linear systems in theory and applications, IEEETransactions on Automatic Control, 19, 1974, 334–348. doi:10.1109/TAC.1974.1100617
  2. [2] R.R. Mohler & W.J. Kolodziej, An overview of bilinear systemtheory and applications IEEE Transactions on Systems, Manand Cybernetics, 10, 1980, 683–688.
  3. [3] R.R. Mohler, Bilinear Control Process (New York: AcademicPress, 1973).
  4. [4] J. Ball & M. Slemrod, Feedback stabilization of distributedsemilinear control systems, J. Appl. Math. Opt., 5, 1979,169–179. doi:10.1007/BF01442552
  5. [5] H.J. Sussmann, Semigroup representations, bilinear approxi-mations of input-output maps, and generalized inputs, in G.Marchesini (Ed.), Mathematical Systems Theory, 172–192.
  6. [6] H. Mabuchi & N. Khaneja, Principles and applications ofcontrol in quantum systems, Int. J. Robust Nonlinear Control.,15, 2005, 647–667. doi:10.1002/rnc.1016
  7. [7] E. Zuazua, Propagation, observation, control and numeri-cal approximation of waves approximated by finite differencemethod, SIAM Review, 47, 2005, 197–243. doi:10.1137/S0036144503432862
  8. [8] V. Jurjevic & J.P. Quinn, Controllability and stability, J. Diff.Equa., 28, 1978, 381–389. doi:10.1016/0022-0396(78)90135-3
  9. [9] J.P. Quinn, Stabilization of bilinear systems by quadraticfeedback control, J. Math. Anal. Appl., 75, 1980, 66–80. doi:10.1016/0022-247X(80)90306-6
  10. [10] M. Slemrod, Stabilization of bilinear control systems withapplications to nonconservative problems in elasticity, SIAMJ. Control Optim, 16 (1), 1978, 131–141. doi:10.1137/0316010
  11. [11] L. Berrahmoune, Stabilization and decay estimate for dis-tributed bilinear systems, Systems Control Letters, 36, 1999,167–171. doi:10.1016/S0167-6911(98)00065-6
  12. [12] E. Zerrik, M. Ouzahra, & K. Ztot, Regional stabilization forinfinite bilinear systems, IEEE Cont. Theory. Appl., 151 (1),2004, 109–116. doi:10.1049/ip-cta:20040017
  13. [13] A. El Jai & S. El Yacoubi, On the number of actuators inparabolic systems, Appl. Math. Comp. Sci., 34, 1993, 673–686.
  14. [14] A. El Jai & A.J. Pritchard, Sensors and actuators in distributedsystems analysis (New York: Wiley, 1988).
  15. [15] Y. Lou & P.D. Christofides, Optimal actuator/sensor placementfor nonlinear control of the Kuramoto-Sivashinsky equation,IEEE Transactions on Control Systems Technology, 11, 2003,737–745. doi:10.1109/TCST.2003.816405
  16. [16] R. Triggiani, On the stabilizability problem in Banach space,J. Math. Anal. Appl., 52, 1975, 383–403. doi:10.1016/0022-247X(75)90067-0
  17. [17] D.G. Aronson & H.F. Weinberger, Multidimensionnal nonlineardiffusions arising in population genetics, Adv. in Math., 30 (1),1978, 33–76. doi:10.1016/0001-8708(78)90130-5

Important Links:

Go Back