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. 
@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://www.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://www.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://www.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://www.numdam.org/item/COCV_2000__5__395_0/

[1] M.A. Aizerman and F.R. Gantmacher, Absolute Stability of Regulator Systems. Holden-Day, San Francisco ( 1964). | MR | Zbl

[2] B.D.O. Anderson and S. Vongpanitlerd, Network Analysis and Synthesis: A Modern Systems Theory Approach. Prentice Hall, Englewood-Cliffs, NJ ( 1973).

[3] V. Barbu, Analysis and Control of Nonlinear Infinite-Dimensional Systems. Academic Press, Boston ( 1993). | MR | Zbl

[4] F. Bucci, 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] F.H. Clarke, Optimization and Nonsmooth Analysis. Wiley, New York ( 1983). | MR | Zbl

[6] F.H. Clarke, Yu.S. Ledyaev, R.J. Stern and P.R. Wolenski, Nonsmooth Analysis and Control Theory. Springer-Verlag, New York ( 1998). | MR | Zbl

[7] C. Corduneanu, Integral Equations and Stability of Feedback Systems. Academic Press, New York ( 1973). | MR | Zbl

[8] C. Corduneanu, Almost Periodic Functions. Wiley, New York ( 1968). | MR | Zbl

[9] R.F. Curtain, H. Logemann, S. Townley and H. Zwart, Well-posedness, stabilizability and admissibility for Pritchard-Salamon systems. Math. Systems, Estimation and Control 7 ( 1997) 439-476. | MR | Zbl

[10] R.F. Curtain and G. Weiss, 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

[11] G. Gripenberg, S.-O. Londen and O. Staffans, Volterra Intgeral and Functional Equations. Cambridge University Press, Cambridge ( 1990). | MR | Zbl

[12] P.R. Halmos, Finite-Dimensional Vector Spaces. Springer-Verlag, New York ( 1987). | MR | Zbl

[13] H.K. Khalil, Nonlinear Systems, 2nd Edition. Prentice-Hall, Upper Saddle River, NJ ( 1996). | Zbl

[14] S. Lefschetz, Stability of Nonlinear Control Systems. Academic Press, New York ( 1965). | MR | Zbl

[15] G.A. Leonov, D.V. Ponomarenko and V.B. Smirnova, Frequency-Domain Methods for Nonlinear Analysis. World Scientific, Singapore ( 1996). | MR | Zbl

[16] B.A.M Van Keulen, H∞-Control for Infinite-Dimensional Systems: A State-Space Approach. Birkhäuser Verlag, Boston ( 1993).

[17] H. Logemann, Circle criteria, small-gain conditions and internal stability for infinite-dimensional systems. Automatica 27 ( 1991) 677-690. | MR | Zbl

[18] H. Logemann and E.P. Ryan, 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

[19] H. Logemann, E.P. Ryan and S. Townley, 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

[20] H. Logemann, E.P. Ryan and S. Townley, Integral control of infinite-dimensional linear systems subject to input saturation. SIAM J. Control Optim. 36 ( 1998) 1940-1961. | MR | Zbl

[21] H. Logemann and S. Townley, Low-gain control of uncertain regular linear systems. SIAM J. Control Optim. 35 ( 1997) 78-116. | MR | Zbl

[22] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York ( 1983). | MR | Zbl

[23] W. Rudin, Functional Analysis. McGraw-Hill, New York ( 1973). | MR | Zbl

[24] D. Salamon, Realization theory in Hilbert space. Math. Systems Theory 21 ( 1989) 147-164. | MR | Zbl

[25] D. Salamon, Infinite-dimensional linear systems with unbounded control and observation: A functional analytic approach. Trans. Amer. Math. Soc. 300 ( 1987) 383-431. | MR | Zbl

[26] O.J. Staffans, Well-Posed Linear Systems, monograph in preparation (preprint available at http://www.abo.fi/-staffans/).

[27] O.J. Staffans, Quadratic optimal control of stable well-posed linear systems. Trans. Amer. Math. Soc. 349 ( 1997) 3679-3715. | MR | Zbl

[28] M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition. Prentice Hall, Englewood Cliffs, NJ ( 1993). | Zbl

[29] G. Weiss, Transfer functions of regular linear systems, Part I: Characterization of regularity. Trans. Amer. Math. Soc. 342 ( 1994) 827-854. | MR | Zbl

[30] G. Weiss, Admissibility of unbounded control operators. SIAM J. Control Optim. 27 ( 1989) 527-545. | MR | Zbl

[31] G. Weiss, Admissibility observation operators for linear semigroups. Israel J. Math. 65 ( 1989) 17-43. | MR | Zbl

[32] G. Weiss, 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] D. Wexler, 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] D. Wexler, Frequency domain stability for a class of equations arising in reactor dynamics. SIAM J. Math. Analysis 10 ( 1979) 118-138. | MR | Zbl