Approximate controllability of the n-th order infinite dimensional systems with controls delayed by the control devices

References

• Bellman , R . 1960 . Introduction to Matrix Analysis , New York : Mcgraw-Hill Book Company .
   Google Scholar
• Balakrishnan , AV . 1998 . Dynamics and Control of Distributed Systems , 121 – 201 . Cambridge : Cambridge University Press .
   Google Scholar
• Jacob , B and Partington , J . 2001 . On the boundedness and continuity of the spectral factorization mapping . SIAM Journal of Control Optimization , 40 : 88 – 106 .
   Google Scholar
• Jacob , B and Partington , JR . 2006 . On controllability of diagonal systems with one-dimensional input space . Systems Control Letters , 55 : 321 – 328 .
   Google Scholar
• Jacob , B and Zwart , H . 1999 . Equivalent conditions for stabilizability of infinite-dimensional systems with admissible control operators . SIAM Journal of Control Optimization , 37 : 1419 – 1455 .
   Google Scholar
• Jacob , B and Zwart , H . 2001 . Exact controllability of diagonal systems with a finite-dimensional output operator . Systems Control Letters , 43 : 101 – 109 .
   Google Scholar
• Jacob , B and Zwart , H . 2004 . Counterexamples concerning observation operators for C 0-semigroups . SIAM Journal of Control Optimization , 43 : 137 – 153 .
   Google Scholar
• Brammer , RF . 1972 . Controllability in linear autonomous systems with positive controllers . SIAM Journal of Control Optimization , 10 : 339 – 353 .
   Web of Science ®Google Scholar
• Burgree , D and Brooklyn , NY . 1951 . “Free vibrations of pin-ended column with distance between pin ends” . Journal of Applied Mechanics , June : 135 – 139 .
   Google Scholar
• Chen , CT . 1970 . Introduction to Linear System Theory , New York, Holt : Rinehart and Winston Inc .
   Google Scholar
• Chen , G and Russel , DL . 1982 . A mathematical model for linear elastic systems with structural damping . Quaterly Applied Mathematics , 39 : 433 – 454 .
   Web of Science ®Google Scholar
• Triggiani , R . 1990 . Gevrey class semigroup arising from elastic systems with gentle dissipation: the case 0 < α < 1/2 . Proceedings of the American Mathematical Society , 100 : 401 – 415 .
   Google Scholar
• Curtain , R and Zwart , H . 1995 . An Introduction to Infinite-Dimensional Linear Systems Theory. Texts in Applied Mathematics. , Vol. 21 , New York : Springer-Verlag .
   Google Scholar
• Davison , EJ and Wang , SH . 1975 . New results on the controllability and observability of general composite systems . IEEE Transactions on Automatic Control , 20 : 123 – 128 .
   Web of Science ®Google Scholar
• Dunford , N and Schwartz , J . 1963 . Linear Operators , Vol. 1 and 2 , New York : Interscience .
   Google Scholar
• Fattorini , HO . 1966 . Some remarks on complete controllability . SIAM Journal of Control Optimization , 4 : 686 – 694 .
   Google Scholar
• Fattorini , HO . 1967 . On complete controllability of linear systems . Journal of Differential Equations , 3 : 391 – 402 .
   Web of Science ®Google Scholar
• Górecki , H . 1986 . Optymalizacja Systemów Dynamicznych , WNT, Warszawa, (in polish)
   Google Scholar
• Hou , S and Pang , W . 2002 . Inversion of confluent vandermonde matrices . An International Journal for Computational Mathematics and Applcations , 43 : 1539 – 1547 .
   Web of Science ®Google Scholar
• Huang , F . 1988 . On the mathematical model with analytic damping . SIAM Journal of Control Optimization. , 26–3 : 714 – 724 .
   Google Scholar
• Ito , K and Kunimatsu , N . 1988 . Stabilization of non-linear distribuded parameter vibratory system . International Journal of Control , 48 : 2389 – 2415 .
   Google Scholar
• Ito , K and Kunimatsu , N . 1991 . Semigroup model of structurally damped timoshenko beam with boundary input . International Journal of Control , 54 : 367 – 391 .
   Web of Science ®Google Scholar
• Kalman , RE . 1960 . On the general theory of control systems, Proceedings I IFAC Congress . 1960 , London. pp. 481 – 493 .
   Google Scholar
• Klamka , J . 1992 . Approximate controllability of second order dynamical systems . Applied Mathematical Computational Science , 2 : 135 – 148 .
   Google Scholar
• Klamka , J . 1991 . Controllability of Dynamical Systems , Dordrecht : Kluwer .
   Google Scholar
• Klamka , J . 1976 . Controllability of linear systems with time-variable delays in control . International Journal of Control , 24 : 869 – 878 .
   Web of Science ®Google Scholar
• Klamka , J . 1977 . Absolute controllability of linear systems with time-variable delays in control . International Journal of Control , 26 : 57 – 63 .
   Web of Science ®Google Scholar
• Respondek , J . 2005a . “Numerical approach to the non-linear diofantic equations with applications to the controllability of infinite dimensional dynamical systems” . International Journal of Control , 78 : 1017 – 1030 .
   Web of Science ®Google Scholar
• Respondek , J . 2005 . Controllability of dynamical systems with constraints . Systems Control Letters , 54/4 : 293 – 314 .
   Google Scholar
• Respondek , J . 2007b . Numerical analysis of controllability of diffusive-convective system with limited manipulating variables . International Communication Heat and Mass Transfer , 34/8 : 934 – 944 .
   Google Scholar
• Sakawa , Y . 1974 . Controllability for partial differential equations of parabolic type . SIAM Journal of Control Optimization , 12 : 389 – 400 .
   Web of Science ®Google Scholar
• Sakawa , Y . 1984 . Feedback control of second order evolution equations with damping . SIAM Journal of Control Optimization , 22 : 343 – 361 .
   Web of Science ®Google Scholar
• Sakawa , Y . 1983 . Feedback stabilization of linear diffusion system . SIAM Journal of Control Optimization , 21 : 667 – 675 .
   Web of Science ®Google Scholar
• Schmitendorf , WE and Barmish , BR . 1980 . Null controllability of linear system with constrained controls . SIAM Journal of Control Optimization , 18 : 327 – 345 .
   Web of Science ®Google Scholar
• Tanabe , H . 1979 . Equations of evolution , London : Pitman .
   Google Scholar
• Triggiani , R . 1975 . Controllability and observability in banach space with bounded operators . SIAM Journal of Control Optimization , 13 : 462 – 491 .
   Web of Science ®Google Scholar
• Zadeh , LA and Desoer , CA . 1963 . Linear System Theory. The State Space Approach , New York : McGraw-Hill .
   Google Scholar