Approximation and decomposition of singularly perturbed stochastic hybrid systems

REFERENCES

• BLANKENSHIP , G. L. , 1974 , Perturbation theory for stochastic ordinary differential equations with applications to optical waveguide analysis . Supplement to IEEE International Symposium on Circuit Theory , pp. 51 - 77 .
   Google Scholar
• BLOM , H. A. P. , 1986 , Overlook potential systems with markovian coefficients . Proceedings of the 25th IEEE Conference on Decision and Control , pp. 1758 - 1764 .
   Google Scholar
• BLOM , H. A. P. , and BAR-SHALOM , Y. , 1988 , The interacting multiple model algorithm for systems with markovian switching parameters . IEEE Transactions on Automatic Control , 33 , 780 - 783 .
   Web of Science ®Google Scholar
• CASTANON , D. A. , CODERCH , M. , LEVY, B. C, and WILLSKY , A. S. , 1980 , Asymptotic analysis, approximation and aggregation methods for stochastic hybrid systems . Proceedings of the 1980 Joint Automatic Control Conference , San Francisco , paper TA3-D .
   Google Scholar
• CLOUTIER , J. R. , EVERS , J. H. , and FEELY , J. J. , 1989 , Assessment of air-to-air missile guidance and control technology . IEEE Control Systems Magazine , pp. 27 - 34 .
   Google Scholar
• CODERCH , M. , WILLSKY , A. S. , SASTRY , S. S. , and CASTANON , D. A. , 1983 , Hierarchical aggregation of singularly perturbed finite state Markov process . Stochastics , 8 , 259 - 289 .
   Google Scholar
• EzzINE , J. , 1989 , On the control and stabilization of hybrid systems. Ph.D. dissertation , Georgia Institute of Technology .
   Google Scholar
• EzzINE , J. , and HADDAD, A. H., 1990 , Error bounds in the averaging of hybrid systems . IEEE Transactions on Automatic Control , 34 , 1188 - 1192 .
   Google Scholar
• GARDINER , C. W. , 1985 , Handbook of Stochastic Methods ( New York Springer-Verlag ).
   Google Scholar
• GEMAN , G. , 1979 , Some averaging and stability results for random differential equations . SIAM Journal on Applied Mathematics , 36 , 86 - 105 .
   Web of Science ®Google Scholar
• GERSTEIN , B. C. , and DYBOWSKI , C. R. , 1985 , Transient Techniques in NMR of Solids ( New York Academic Press ).
   Google Scholar
• HECK , B. S. , and HADDAD , A. H. , 1988 , Singular perturbation analysis of linear systems with scalar quantized control . Automatica , 24 , 755 - 764 .
   Web of Science ®Google Scholar
• HOEL , P. G. , PORT, S. C, and STONE , C. J. , 1972 , Introduction to Stochastic Processes ( Boston Houghton Mifflin ).
   Google Scholar
• JOSE , M. V. , and HADDAD , A. H. , 1987 , On singularly perturbed switched parameter systems . Proceedings of the 6th American Control Conference , Minneapolis , pp. 424 - 425 .
   Google Scholar
• KEILSON , J. , 1979 , Markov Chain Models-Rarity and Exponentiality ( New York Springer-Verlag ).
   Google Scholar
• KEILSON , J. , and RAO , S. S. , 1970 , RA process with chain dependent growth rates . Journal of Applications , 7 , 699 - 711 .
   Google Scholar
• KHAS'MINSKII , R. Z. , 1966 , On stochastic process defined by differential equations with a small parameter . Theoretical Probability Applications , XI , 211 - 228 .
   Google Scholar
• KLOSEK , M. M. , MATKOWSKY , B. J. , and SHUSS , Z. , 1989 , First-order dynamics driven by rapid markovian jumps . SIAM Journal of Applied Mathematics , 49 , 1811 - 1833 .
   Google Scholar
• KOKOTOVIC , P. V. , and KHALIL , H. K. , 1986 , Singular Perturbations in Systems and Control ( New York IEEE Press ).
   Google Scholar
• KOKOTOVIC , P. V. , O'MALLEY , R. E. , JR. , and SANNUTI , P. , 1976 , Singular perturbation and order reduction in control theory-an overview . Automatica , 12 , 123 - 132 .
   Web of Science ®Google Scholar
• LOAD , C. V. , 1977 , The sensitivity of the matrix exponential. Journal of Numerical Analysis , 14 , 971 - 981 .
   Google Scholar
• LOPARO , K. A. , ROTH , Z. , and ECKERT , S. J. , 1986 , Nonlinear filtering for systems with random structure . IEEE Transactions on Automatic Control , 31 , 1064 - 1068 .
   Google Scholar
• MAGNUS , M. , 1954 , On the exponential solution of differential equations for a linear operator . Communications in Pure and Applied Mathematics , 7 , 649 - 673 .
   Web of Science ®Google Scholar
• NAYFEH , A. H. , 1981 , Introduction to Pertubalion Techniques ( New York Wiley ).
   Google Scholar
• PAPANICOLAOU , G. C. , and KOHLER , W. , 1974 , Asymptotic theory of mixing stochastic ordinary differential equations . Communications in Pure and Applied Mathematics , 27 , 641 - 668 .
   Web of Science ®Google Scholar
• PHILLIPS , R. G. , and KOKOTOVIC , P. V. , 1981 , A single perturbation approach to modeling and control of Markov chains . IEEE Transactions on Automatic Control , 26 , 1087 - 1094 .
   Google Scholar
• SAKSENA , V. R. , O'REILLY , J. , and KOKOTOVIC , P. V. , 1984 , Singular perturbations and time-scale methods in control theory survey, 1976-1983 . Automatica , 20 , 273 - 293 .
   Web of Science ®Google Scholar
• STORM , T. , 1975 , On logarithmic norm . Journal of Numerical Analysis , 12 , 741 - 753 .
   Google Scholar
• SWORDER , D. D. , and R. O. ROGERS , R. O., 1983 , An LQ solution to a control problem associated with a solar thermal central receiver . IEEE Transactions on Automatic Control , 28 , 971 - 978 .
   Web of Science ®Google Scholar
• TSAI , C. C. , and HADDAD , A. H. , 1990 , On singularly perturbed hybrid systems . Proceedings 24th Annual Conference on Information Science and Systems , Princeton University , pp. 455 - 459 ; 1991, Analysis of singularly perturbed stochastic hybrid systems. Proceedings of the 10th American Control Conference, Boston, pp. 1563-1568 .
   Google Scholar
• VlDYASAGAR , M. , 1978 , Nonlinear System Analysis ( Englewood Cliffs , NJ Prentice Hall ).
   Google Scholar
• WILCOX , R. M. , 1967 , Exponential operators and parameter differentiation in quantum physics . Journal of Mathematical Physics , 8 , 962 - 982 .
   Web of Science ®Google Scholar