A Rational Decay Rate for Infinite Bilinear Parabolic Systems

Azzeddine Tsouli(1*), Ali Boutoulout(2)

(1) TSI Team MACS Laboratory Moulay Ismail University. Faculty of Sciences. Box 11201 Zitoune, Meknes, Morocco
(2) TSI Team MACS Laboratory Moulay Ismail University. Faculty of Sciences. Box 11201 Zitoune, Meknes,
(*) Corresponding author

DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)


In this paper, we will study the strong stability for distributed bilinear systems with decay rate estimate based on the decomposition of the state space via the spectral properties of the systems.  An illustrating example and simulations are provided.

Copyright © 2014 Praise Worthy Prize - All rights reserved.


Bilinear Parabolic Systems; Stabilization; Polynomial Decay Estimate

Full Text:



K. Ammari and M. Tucsnak. Stabilization of second order evolution equations by a class of unbounded feedbacks, ESAIM Control . Cal. Var., 6, 2001, pp. 361-386.

J. Ball and M. Slemrod. Feedback stabilization of distributed semilinear control systems, J. Appl. Math.Opt. 5, 1979, pp. 169-179.

C. Bruni, G. Dipillo and G. Koch. Bilinear systems: An appealing class of nearly linear systems in theory and applications, IEEE Transactions on Automatic Control. 19, 1974, pp. 334-348.

M.S. Chen. Exponential stabilization of a constrained bilinear system. Automatica., 34, 1998, pp. 989-992.

L. Guo and H. Schwarz. A Control Scheme for Bilinear Systems and Application to a Secondary Controlled Hydraulic Rotary Drive,. in Proc. of the 28th IEEE Conference on Decision and Control, Tampa, Florida, 1989.

T. Kato. Perturbation theory for linear operators. New York. Springer, 1980.

R.R. Mohler. Bilinear Control Processe. Academic Press, New York, 1973.

R. R. Mohler and A. Y. Khapalov. Bilinear control and application to exible a.c. Transmission Systems. Journal of Optimization Theory and Applications, 2000, pp. 621-637.

M. Ouzahra. Strong stabilization with decay estimate of semilinear systems. Systems and Control Letters, 57, 2008, pp. 813-815.

M. Ouzahra. Stabilisation of in_nite-dimensional bilinear systems using a quadratic feedback control. International Journal of Control, 2009, pp. 1-8.

M. Ouzahra. Exponential and Weak Stabilization of Constrained Bilinear Systems. SIAM J. Control Optim., 48, Issue 6 ,2010, pp. 3962-3974.

M. Ouzahra. Feedback stabilization of parabolic systems with bilinear controls. Electron. J. Di_. Equ. 38, 2011, pp. 1-10.

M. Ouzahra, A. Tsouli, A. Boutoulout. Stabilisation and polynomial decay estimate for distributed semilinear systems, Internat. J. Con- trol 85, 2012, no. 4, pp. 451-456.

A. Pazy. Semi-groups of linear operators and applications to partial differential equations. Springer Verlag, New York, 1983.

J. P. Quinn. Stabilization of bilinear systems by quadratic feedback control. J. Math. Anal. Appl, 75, 1980, pp. 66-80.

R. Triggiani. On the stabilizability problem in Banach space. J. Math. Anal. Appl, 52, 1975, pp. 383-403.

A. Tsouli, M. Ouzahra and A. Boutoulout. A Decay Estimate for Constrained Semilinear Systems. Inf. Sci. Lett. 3, No. 2, 2014, pp. 77-83.


  • There are currently no refbacks.

Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2021 Praise Worthy Prize