@article{COCV_2000__5__395_0, author = {Logemann, Hartmut and Curtain, Ruth F.}, title = {Absolute stability results for well-posed infinite-dimensional systems with applications to low-gain integral control}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {395--424}, publisher = {EDP-Sciences}, volume = {5}, year = {2000}, mrnumber = {1778393}, zbl = {0964.93048}, language = {en}, url = {http://archive.numdam.org/item/COCV_2000__5__395_0/} }
TY - JOUR AU - Logemann, Hartmut AU - Curtain, Ruth F. TI - Absolute stability results for well-posed infinite-dimensional systems with applications to low-gain integral control JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2000 SP - 395 EP - 424 VL - 5 PB - EDP-Sciences UR - http://archive.numdam.org/item/COCV_2000__5__395_0/ LA - en ID - COCV_2000__5__395_0 ER -
%0 Journal Article %A Logemann, Hartmut %A Curtain, Ruth F. %T Absolute stability results for well-posed infinite-dimensional systems with applications to low-gain integral control %J ESAIM: Control, Optimisation and Calculus of Variations %D 2000 %P 395-424 %V 5 %I EDP-Sciences %U http://archive.numdam.org/item/COCV_2000__5__395_0/ %G en %F COCV_2000__5__395_0
Logemann, Hartmut; Curtain, Ruth F. Absolute stability results for well-posed infinite-dimensional systems with applications to low-gain integral control. ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 395-424. http://archive.numdam.org/item/COCV_2000__5__395_0/
[1] Absolute Stability of Regulator Systems. Holden-Day, San Francisco ( 1964). | MR | Zbl
and ,[2] Network Analysis and Synthesis: A Modern Systems Theory Approach. Prentice Hall, Englewood-Cliffs, NJ ( 1973).
and ,[3] Analysis and Control of Nonlinear Infinite-Dimensional Systems. Academic Press, Boston ( 1993). | MR | Zbl
,[4] Frequency-domain stability of nonlinear feedback systems with unbounded input operator. Preprint. Dipartimento de Matematica Applicata "G. Sansone", Università degli Studi di Firenze ( 1997) (to appear in Dynamics of Continuous, Discrete and Impulsive Systems). | MR | Zbl
,[5] Optimization and Nonsmooth Analysis. Wiley, New York ( 1983). | MR | Zbl
,[6] Nonsmooth Analysis and Control Theory. Springer-Verlag, New York ( 1998). | MR | Zbl
, , and ,[7] Integral Equations and Stability of Feedback Systems. Academic Press, New York ( 1973). | MR | Zbl
,[8] Almost Periodic Functions. Wiley, New York ( 1968). | MR | Zbl
,[9] Well-posedness, stabilizability and admissibility for Pritchard-Salamon systems. Math. Systems, Estimation and Control 7 ( 1997) 439-476. | MR | Zbl
, , and ,[10] Well-posedness of triples of operators in the sense of linear systems theory, in Control and Estimation of Distributed Parameter System, edited by F. Kappel, K. Kunisch and W. Schappacher. Birkhäuser Verlag, Basel ( 1989) 41-59. | MR | Zbl
and ,[11] Volterra Intgeral and Functional Equations. Cambridge University Press, Cambridge ( 1990). | MR | Zbl
, and ,[12] Finite-Dimensional Vector Spaces. Springer-Verlag, New York ( 1987). | MR | Zbl
,[13] Nonlinear Systems, 2nd Edition. Prentice-Hall, Upper Saddle River, NJ ( 1996). | Zbl
,[14] Stability of Nonlinear Control Systems. Academic Press, New York ( 1965). | MR | Zbl
,[15] Frequency-Domain Methods for Nonlinear Analysis. World Scientific, Singapore ( 1996). | MR | Zbl
, and ,[16] H∞-Control for Infinite-Dimensional Systems: A State-Space Approach. Birkhäuser Verlag, Boston ( 1993).
,[17] Circle criteria, small-gain conditions and internal stability for infinite-dimensional systems. Automatica 27 ( 1991) 677-690. | MR | Zbl
,[18] Time-varying and adaptive integral control of innnite-dimensional regular linear systems with input nonlinearities. SIAM J. Control Optim. 38 ( 2000) 1120-1144. | MR | Zbl
and ,[19] Integral control of linear systems with actuator nonlinearities: lower bounds for the maximal regulating gain. IEEE Trans. Auto. Control 44 ( 1999) 1315-1319. | MR | Zbl
, and ,[20] Integral control of infinite-dimensional linear systems subject to input saturation. SIAM J. Control Optim. 36 ( 1998) 1940-1961. | MR | Zbl
, and ,[21] Low-gain control of uncertain regular linear systems. SIAM J. Control Optim. 35 ( 1997) 78-116. | MR | Zbl
and ,[22] Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York ( 1983). | MR | Zbl
,[23] Functional Analysis. McGraw-Hill, New York ( 1973). | MR | Zbl
,[24] Realization theory in Hilbert space. Math. Systems Theory 21 ( 1989) 147-164. | MR | Zbl
,[25] Infinite-dimensional linear systems with unbounded control and observation: A functional analytic approach. Trans. Amer. Math. Soc. 300 ( 1987) 383-431. | MR | Zbl
,[26] Well-Posed Linear Systems, monograph in preparation (preprint available at http://www.abo.fi/-staffans/).
,[27] Quadratic optimal control of stable well-posed linear systems. Trans. Amer. Math. Soc. 349 ( 1997) 3679-3715. | MR | Zbl
,[28] Nonlinear Systems Analysis, 2nd Edition. Prentice Hall, Englewood Cliffs, NJ ( 1993). | Zbl
,[29] Transfer functions of regular linear systems, Part I: Characterization of regularity. Trans. Amer. Math. Soc. 342 ( 1994) 827-854. | MR | Zbl
,[30] Admissibility of unbounded control operators. SIAM J. Control Optim. 27 ( 1989) 527-545. | MR | Zbl
,[31] Admissibility observation operators for linear semigroups. Israel J. Math. 65 ( 1989) 17-43. | MR | Zbl
,[32] The representation of regular linear systems on Hilbert spaces, in Control and Estimation of Distributed Parameter System, edited by F. Kappel, K. Kunisch and W. Schappacher. Birkhäuser Verlag, Basel ( 1989) 401-416. | MR | Zbl
,[33] On frequency domain stability for evolution equations in Hilbert spaces via the algebraic Riccati equation. SIAM J. Math. Analysis 11 ( 1980) 969-983. | MR | Zbl
,[34] Frequency domain stability for a class of equations arising in reactor dynamics. SIAM J. Math. Analysis 10 ( 1979) 118-138. | MR | Zbl
,