### A Rational Decay Rate for Infinite Bilinear Parabolic Systems

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#### Abstract

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.

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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.

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