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Original Articles

Strong stabilisation and decay estimate for unbounded bilinear systems

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Pages 1497-1505 | Received 19 Aug 2011, Accepted 01 May 2012, Published online: 29 May 2012

References

  • Babkin , B . 1953 . On a Generalisation of a Theorem of Academician S.A. Caplygin on a Differential Inequality . Molotov. Gos. Univ. Uc. , 8 : 3 – 6. . (in Russian)
  • Ball , J and Slemrod , M . 1979 . Feedback Stabilisation of Distributed Semilinear Control Systems . Journal of Applied Mathematics and Optimmization , 5 : 169 – 179 .
  • Benbrik , A . 1987 . “ Contrôle Optimal des Systèmes à Paramètres répartis Bilinéaires ” . Doctorat : Perpignan University .
  • Berrahmoune , L . 1999 . Stabilization and Decay Estimate for Distributed Bilinear Systems . Systems Control Letters , 36 : 167 – 171 .
  • Berrahmoune , L . 2009 . A Note on Admissibility for Unbounded Bilinear Control Systems . Bulletin of the Belgian Mathematical Society Simon Stevin , 16 : 193 – 204 .
  • Berrahmoune , L . 2010 . Stabilization of Unbounded Bilinear Control Systems in Hilbert Space . Journal of Mathematical Analysis and Applications , 372 : 645 – 655 .
  • Bounit , H and Hammouri , H . 1999 . Feedback Stabilisation for a Class of Distributed Semilinear Control Systems . Nonlinear Analysis , 37 : 953 – 969 .
  • Bounit , H and Idrissi , A . 2005 . Regular Bilinear Systems . IMA Journal of Mathematical Control and Information , 22 : 26 – 57 .
  • Brezis , H . 1966 . Opérateurs Monotones . Séminaire Choquet, Initiation á l'Analyse , 2 : 1 – 33 .
  • Brezis , H . 1968 . Equations et Inéquations non Linéaires Dans Les Espaces Vectorièls en Dualité . Annales De l'institut Fourier , 18 : 115 – 175 .
  • Brezis , H . 1973 . Opérateurs Maximaux Monotones et Semi-groupes de Contractions Dans les Espaces de Hilbert, Mathematical Studies , Vol. 5 , North-Holland : Amsterdam .
  • Brezis , H . 1983 . Analyse Fonctionnelle. Théorie et Applications , Paris : Masson .
  • Bruni , C , Dipillo , G and Koch , G . 1974 . Bilinear Systems: An Appealing Class of Nearly Linear Systems in Theory and Applications . IEEE Transactions on Automatic Control , 19 : 334 – 348 .
  • El Alami , N . 1986 . “ Analyse et Commande Optimale des Systèmes Bilinéaires Distribués, Application Aux Procédés énergétiques ” . In Doctorat d'état , IMP Perpignan .
  • Gronwall , TH . 1919 . Note on the Derivatives with Respect to a Parameter of the Solutions of a System of Differential Equations . Annals of Mathematics , 20 : 293 – 296 .
  • Idrissi , A . 2003 . On the Unboundedness of Control Operators for Bilinear Systems . Questions Mathematicae , 26 : 105 – 123 .
  • Idrissi , A and Bounit , H . 2008 . Time-varying Bilinear Systems . SIAM Journal of Control and Optimization , 47 : 1097 – 1126 .
  • Kato , T . 1980 . Perturbation Theory for Linear Operators , New York : Springer .
  • Khapalov , AY and Mohler , RR . 2000 . Bilinear Control and Application to Flexible A.C. Transmission Systems . Journal of Optimization Theory and Applications , 105 : 621 – 637 .
  • Lasiecka , I and Tataru , D . 1993 . Uniform Boundary Stabilisation of Semilinear Wave Equation with Nonlinear Boundary Damping . Journal of Differential and Integral Equations , 6 : 507 – 533 .
  • Li , ZG , Wen , CY and Soh , YC . 2001 . Switched Controllers and their Applications in Bilinear Systems . Automatica , 37 : 477 – 481 .
  • Luo , ZH , Guo , BZ and Morgul , O . 1998 . Stability and Stabilisation of Infinite-dimensional Systems with Applications , London : Springer-Verlag .
  • Mohler , RR . 1973 . Bilinear Control Processe , New York : Academic Press .
  • Mohler , RR and Kolodziej , WJ . 1980 . An Overview of Bilinear System Theory and Applications . IEEE Transactions on Systems, Man and Cybernetics , 10 : 683 – 688 .
  • Ouzahra , M . 2008 . Strong Stabilisation with Decay Estimate of Semilinear Systems . Systems & Control Letters , 57 : 813 – 815 .
  • Ouzahra , M . 2009 . Stabilisation of Infinite-dimensional Bilinear Systems using a Quadratic Feedback Control . International Journal of Control , 82 : 1657 – 1664 .
  • Triggiani , R . 1975 . On the Stabilisability Problem in Banach Space . Journal of Mathematical Analysis and Application , 52 : 383 – 403 .
  • Willet , D and Wong , J . 1965 . On the Discrete Analogues of Some Generalisations of Gronwall's Inequality . Monatshefte für Mathematik , 69 : 362 – 367 .

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