Feedback stabilization and adaptive stabilization of stochastic nonlinear systems by the control Lyapunov function

References

• Abedi , F. , Abu Hassan , M. and Arifin , N.M. 2011 . Control Lyapunov function for feedback stabilization of affine in the control stochastic time-varying systems . Int. J. Math. Anal. , 5 ( 4 ) : 175 – 188 .
   Google Scholar
• Artstein , Z. 1983 . Stabilization with relaxed controls . Nonlinear Anal. , 7 : 1163 – 1173 .
   Google Scholar
• Deng , H. , Krstic , M. and Williams , R.J. 2001 . Stabilization of stochastic nonlinear systems driven by noise of unknown covariance . Trans. Automat. Control , 46 ( 8 ) : 1237 – 1253 .
   Google Scholar
• Florchinger , P. 1993 . A universal formula for the stabilization of control stochastic differential equations . Stoch. Anal. Appl. , 11 ( 2 ) : 155 – 162 .
   Google Scholar
• Florchinger , P. 1995 . Lyapunov-like techniques for stochastic stability . SIAM J. Control Optim. , 33 : 1151 – 1169 .
   Google Scholar
• Florchinger , P. 2000 . Application of stochastic Artstein's theorem to feedback stabilization . Stoch. Anal. Appl. , 18 ( 3 ) : 361 – 373 .
   Google Scholar
• Florchinger , P. 2001 . A stochastic Jurdjevic–Quinn theorem for the stabilization of nonlinear stochastic differential systems . Stoch. Anal. Appl. , 19 ( 3 ) : 473 – 480 .
   Google Scholar
• Florchinger , P. 2003 . Stabilization of passive nonlinear stochastic differential systems by bounded feedback . Stoch. Anal. Appl. , 21 : 1255 – 1282 .
   Google Scholar
• Handel , R.V. 2006 . Almost global stochastic stability . SIAM J. Control Optim. , 45 : 1297 – 1313 .
   Google Scholar
• Jurdjevic , V. and Quinn , J.P. 1978 . Controllability and stability . J. Differential Equations , 28 : 381 – 389 .
   Google Scholar
• Khasminskii , R.Z. 1980 . Stochastic Stability of Differential Equation , The Netherlands : Sijthoff Noordhoff, Alphen aan den Rijn .
   Google Scholar
• Kolmanovskii , V.B. and Shaikhet , L.E. 1995 . A method for constructing Lyapunov functionals for stochastic differential equations of neutral type . Differ. Uravn , 31 : 1851 – 1857 . (in Russian); Differential Equations. 31 (1941), pp. 1819–1825 (in English)
   Google Scholar
• Krstic , M. and Deng , H. 1998 . Stabilization of Uncertain Nonlinear Systems , New York : Springer .
   Google Scholar
• Krstic , M. and Kokotovic , P. 1995 . Control Lyapunov function for adaptive nonlinear stabilization . Syst. Control Lett. , 26 : 17 – 23 .
   Google Scholar
• Krstic , M. , Kanellakopoulos , L. and Kokotovic , P. 1992 . Adaptive nonlinear control without overparameterization . Syst. Control Lett. , 19 : 177 – 185 .
   Google Scholar
• Kushner , H.J. 1967 . Converse theorems for stochastic Lyapunov functions . SIAM J. Control Optim. , 5 : 228 – 233 .
   Google Scholar
• Kushner , H.J. 1972 . Stochastic Stability, in Stability of Stochastic Dynamical Systems , Lecture notes in Math Edited by: Curtain , R. 97 – 124 . New York : Springer-Verlag .
   Google Scholar
• Massera , J.L. 1949 . On Liapunov's conditions of stability . Ann. Math. , 50 : 705 – 721 .
   Google Scholar
• Massera , J.L. 1956 . Contributions to stability theory . Ann. Math. , 64 : 182 – 206 . erratum in Ann. Math. 68 (1958), p. 202
   Google Scholar
• Rogers , L.C.G. and Williams , D. 1994 . Diffusions, Markov Processes and Martingales , 2nd ed. , 1 New York : Wiley .
   Google Scholar
• Shaikhet , L. 2010 . Some new aspects of Lyapunov-type theorem for stochastic differential equations of neutral type . SIAM J. Control Optim. , 48 ( 7 ) : 4481 – 4499 .
   Google Scholar
• Sontag , E. 1989 . A universal construction of Artstein's theorem on nonlinear stabilization . Syst Control Lett. , 13 : 117 – 123 .
   Google Scholar
• Tsinias , J. 1991 . Existence of control Lyapunov functions and applications to state feedback stabilizability of nonlinear systems . SIAM J. Control Optim. , 29 : 457 – 473 .
   Google Scholar
• Wilson , F.W. 1966 . Smoothing Derivatives of Functions and Applications , Tech. Report 66–3 413 – 428 . Providence, RI : Brown University .
   Google Scholar
• Wilson , F.W. 1967 . The structure of the level surfaces of a Lyapunov function . J. Differential. Equations , 3 : 323 – 329 .
   Google Scholar