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},
zbl = {0964.93048},
mrnumber = {1778393},
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
DA  - 2000///
SP  - 395
EP  - 424
VL  - 5
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/COCV_2000__5__395_0/
UR  - https://zbmath.org/?q=an%3A0964.93048
UR  - https://www.ams.org/mathscinet-getitem?mr=1778393
LA  - en
ID  - COCV_2000__5__395_0
ER  - 
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 183556 | Zbl 0123.28401

[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 1195128 | Zbl 0776.49005

[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 1774950 | Zbl 0966.93089

[5] F.H. Clarke, Optimization and Nonsmooth Analysis. Wiley, New York ( 1983). | MR 709590 | Zbl 0582.49001

[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 1488695 | Zbl 1047.49500

[7] C. Corduneanu, Integral Equations and Stability of Feedback Systems. Academic Press, New York ( 1973). | MR 358245 | Zbl 0273.45001

[8] C. Corduneanu, Almost Periodic Functions. Wiley, New York ( 1968). | MR 481915 | Zbl 0175.09101

[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 1472401 | Zbl 0815.93046

[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 1033051 | Zbl 0686.93049

[11] G. Gripenberg, S.-O. Londen and O. Staffans, Volterra Intgeral and Functional Equations. Cambridge University Press, Cambridge ( 1990). | MR 1050319 | Zbl 0695.45002

[12] P.R. Halmos, Finite-Dimensional Vector Spaces. Springer-Verlag, New York ( 1987). | MR 409503 | Zbl 0288.15002

[13] H.K. Khalil, Nonlinear Systems, 2nd Edition. Prentice-Hall, Upper Saddle River, NJ ( 1996). | Zbl 1003.34002

[14] S. Lefschetz, Stability of Nonlinear Control Systems. Academic Press, New York ( 1965). | MR 175676 | Zbl 0136.08801

[15] G.A. Leonov, D.V. Ponomarenko and V.B. Smirnova, Frequency-Domain Methods for Nonlinear Analysis. World Scientific, Singapore ( 1996). | MR 1409144 | Zbl 0954.65091

[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 1113737 | Zbl 0749.93073

[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 1760063 | Zbl 0968.93074

[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 1689160 | Zbl 0955.93018

[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 1638027 | Zbl 0913.93031

[21] H. Logemann and S. Townley, Low-gain control of uncertain regular linear systems. SIAM J. Control Optim. 35 ( 1997) 78-116. | MR 1430284 | Zbl 0873.93044

[22] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York ( 1983). | MR 710486 | Zbl 0516.47023

[23] W. Rudin, Functional Analysis. McGraw-Hill, New York ( 1973). | MR 365062 | Zbl 0253.46001

[24] D. Salamon, Realization theory in Hilbert space. Math. Systems Theory 21 ( 1989) 147-164. | MR 977021 | Zbl 0668.93018

[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 876460 | Zbl 0623.93040

[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 1407712 | Zbl 0889.49023

[28] M. Vidyasagar, Nonlinear Systems Analysis, 2nd Edition. Prentice Hall, Englewood Cliffs, NJ ( 1993). | Zbl 0759.93001

[29] G. Weiss, Transfer functions of regular linear systems, Part I: Characterization of regularity. Trans. Amer. Math. Soc. 342 ( 1994) 827-854. | MR 1179402 | Zbl 0798.93036

[30] G. Weiss, Admissibility of unbounded control operators. SIAM J. Control Optim. 27 ( 1989) 527-545. | MR 993285 | Zbl 0685.93043

[31] G. Weiss, Admissibility observation operators for linear semigroups. Israel J. Math. 65 ( 1989) 17-43. | MR 994732 | Zbl 0696.47040

[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 1033074 | Zbl 0685.93040

[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 595824 | Zbl 0488.34054

[34] D. Wexler, Frequency domain stability for a class of equations arising in reactor dynamics. SIAM J. Math. Analysis 10 ( 1979) 118-138. | MR 516758 | Zbl 0404.45016