Stability and stabilizability of stochastic evolution equations on Hilbert spaces

REFERENCES

• Bachman , G. , and Narici , L. , 1966 , Functional Analysis , ( New York : Academic Press ).
   Google Scholar
• Balakrishnan , A. V. , 1981 , Applied Functional Analysis, second edition , ( New York : Springer-Verlag ).
   Google Scholar
• Curtain , R. F. , 1981 , Stability of stochastic partial differential equations. Journal of Mathematical Analysis and Applications , 79 , 352 – 369 .
   Web of Science ®Google Scholar
• Curtain , R. F. , and Falb , P. L. , 1970 , Ito's lemma in infinite dimensions. Journal of Mathematical Analysis and Applications , 31 , 434 – 448 .
   Web of Science ®Google Scholar
• Curtain , R. F. , and Pritchard , A. , 1978 , Infinite Dimensional Linear Systems Theory , ( New York : Springer-Verlag ).
   Google Scholar
• Datko , R. , 1970 , Extending a theorem of A. M. Liapunov to Hilbert space. Journal of Mathematical Analysis and Applications , 32 , 610 – 616 .
   Google Scholar
• Deimling , K. , 1985 , Nonlinear Functional Analysis , ( New York : Springer-Verlag ).
   Google Scholar
• Dieudonne , J. , 1969 , Foundation of Modern Analysis , ( New York : Academic Press ).
   Google Scholar
• Gao , Z. Y. , and Ahmed , N. U. , 1986 , Stabilizability of certain stochastic systems. International Journal of Systems Science , 17 , 1175 – 1185 .
   Web of Science ®Google Scholar
• Haussmann , U. G. , 1971 , Optimal stationary control with state and control dependent noise. SIAM Journal of Control , 9 , 184 – 198 ; 1973 , Stability of linear systems with control dependent noise. Ibid. , 11 , 382 – 394 ; 1978 , Asymptotic stability of the linear Ito Equation in infinite dimensions. Journal of Mathematical Analysis and Applications , 65 , 219 – 235 .
   Google Scholar
• Ichikawa , A. , 1979 , Dynamic programming approach to stochastic evolution equations. SIAM Journal of Control and Optimization , 17 , 152 – 174 ; 1982 , Stability of semilinear stochastic evolution equations. Journal of Mathematical Analysis and Applications , 90 , 12 – 44 ; 1984 , Equivalence of Lip stability and exponential stability for a class of nonlinear semigroups. Nonlinear Analysis, Theory, Methods, and Application , 8 , 805 – 815 .
   Web of Science ®Google Scholar
• Kato , T. , 1976 , Perturbation Theory for Linear Operators, second edition , ( New York : Springer-Verlag ).
   Google Scholar
• Mahalanbis , A. K. , and Purkayastha , S. , 1973 , I.E.E.E. Transactions on Automatic Control , 18 , 266 .
   Google Scholar
• Mohler , R. R. , and Kolodzjej , W. J. , 1980 , An overview of bilinear system theory and applications. I.E.E.E. Transactions on Systems Man and Cybernetics , 10 , 683 – 688 .
   Web of Science ®Google Scholar
• Willems , J. L. , 1973 , Mean square stability criteria for stochastic feedback systems. International Journal of Systems Science , 4 , 545 – 564 .
   Google Scholar
• Willems , J. L. , and Willems , J. C. , 1976 , Feedback stabilizability for stochastic systems with state and control dependent noise. Automatica , 12 , 277 – 283 .
   Web of Science ®Google Scholar
• Wonham , W. M. , 1974 , Probabilistic Methods in Applied Mathematics , edited by A. T. Bharucha-Reid , Vol. 2 ( New York : Academic Press ), p. 132 .
   Google Scholar
• Zabczyk , K. , 1979 , Probability Theory , edited by Z. Ciesielski , Vol. 5 ( Warsaw : Center Publications ), p. 273 .
   Google Scholar