Output regulation for linear systems with anti-stable eigenvalues in the presence of input saturation

Corresponding Author

Raffaella De Santis

[email protected]

Dipartimento di Informatica e Sistemistica, Università degli Studi di Roma “La Sapienza” via Eudossiana 18, 00184 Roma, Italy

Dipartimento di Informatica e Sistemistica, Università degli Studi di Roma “La Sapienza”, via Eudossiana 18, 00184 Roma, Italy===Search for more papers by this author

Raffaella De Santis,

Corresponding Author

Raffaella De Santis

[email protected]

Dipartimento di Informatica e Sistemistica, Università degli Studi di Roma “La Sapienza” via Eudossiana 18, 00184 Roma, Italy

Dipartimento di Informatica e Sistemistica, Università degli Studi di Roma “La Sapienza”, via Eudossiana 18, 00184 Roma, Italy===Search for more papers by this author

First published: 03 April 2000

https://doi.org/10.1002/(SICI)1099-1239(20000430)10:5<423::AID-RNC481>3.0.CO;2-J

Citations: 7

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Abstract

This paper studies the problem of output regulation for linear systems in the presence of input saturation in the full information case. It is assumed that the dynamic matrix has anti-stable eigenvalues and the class of disturbance and/or reference signals consists of constant, sinusoidal and zero mean periodic signals. Nonlinear control laws are used, which enlarge—with respect to what can be obtained using a linear control law—the set of initial conditions (of the plant and the exosystem) for which the problem is solvable. An explicit expression of this set is also given. Copyright © 2000 John Wiley & Sons, Ltd.

REFERENCES

1 Teel AR. A nonlinear control viewpoint on anti-windup and related problems. Preprints of the 4th IFAC NOLCOS, 1998; 115–120.
Google Scholar
2 Sontag ED, Sussmann HJ. Nonlinear output feedback design for linear system with saturated controls. Proceedings of 29th IEEE Conference on Decision and Control, Honolulu 1990; 3414–3416.
Google Scholar
3 Teel AR. Global stabilization and tracking for multiple integrators. Systems and Control Letters 1992; 18: 165–171.
10.1016/0167-6911(92)90001-9
Web of Science® Google Scholar
4 Sussmann HJ, Sontag ED, Yang Y. A general result on the stabilization of linear systems using bounded controls. IEEE Transactions on Automatic Control 1994; AC 39: 2411–2425.
10.1109/9.362853
Web of Science® Google Scholar
5 Teel AR. A nonlinear small gain theorem for the analysis of control systems. IEEE Transactions on Automatic Control 1996; AC 41: 1256–1270.
10.1109/9.536496
Web of Science® Google Scholar
6 Fuller AT. In the large stability of relay and saturated control systems with linear controllers. International Journal of Control 1969; 10: 457–480.
10.1080/00207176908905846
Web of Science® Google Scholar
7 Sussmann HJ, Yang Y. On the stabilizability of multiple integrators with bounded controls. Proceedings of IEEE Conference on Decision and Control, Brighton, UK, 1991; 70–73.
Google Scholar
8 Lin Z, Saberi A. A semi-global low-and-high gain design technique for linear systems with input saturation—stabilization and disturbance rejection. International Journal of Robust and Nonlinear Control 1995; 5: 219–226.
10.1002/rnc.4590050503
Web of Science® Google Scholar
9 Lin Z. H_∞-almost disturbance decoupling with internal stability for linear systems subject to input saturation. Proceedings of 35th Conference on Decision and Control, 1996.
Google Scholar
10 Lin Z, Stoorvogel AA, Saberi A. Output regulation for linear systems subject to input saturation. Automatica 1996; 32: 29–47.
10.1016/0005-1098(95)00110-7
Web of Science® Google Scholar
11 De Santis R, Isidori A. Output regulation for linear systems with anti-stable eigenvalues in the presence of input saturation. Proceedings 38th IEEE Conference on Decision and Control, Phoenix, Arizona, 1999.
Google Scholar
12 De Santis R, Isidori A. On the output regulation for linear systems in the presence of input saturation. 1999; submitted.
Google Scholar
13 Francis BA. The linear multivariable regulator problem. SIAM Journal on Control and Optimization 1975; 15: 486–505.
10.1137/0315033
Web of Science® Google Scholar
14 De Santis R, Isidori A. The problem of output regulation for a class of linear systems subject to saturating actuators. Proceedings of European Control Conference ECC 99, Karlsruhe, Germany, 1999.
Google Scholar
15 Lin Z, Pachter M, Banda S. Toward improvement of tracking performance—nonlinear feedback for linear systems. International Journal of Control 1998; 70: 1–11.
10.1080/002071798222433
Web of Science® Google Scholar
16 Isidori A, Byrnes CI. Output regulation of nonlinear systems. IEEE Transactions on Automatic Control 1990; AC 35: 131–140.
10.1109/9.45168
Web of Science® Google Scholar
17 Isidori A. Nonlinear Control Systems, ( 3rd edn.) Springer: London, 1995.
10.1007/978-1-84628-615-5
Google Scholar
18 Teel AR, Peuteman J, Aeyels D. Global asymptotic stability for the averaged implies semi-global practical asymptotic stability for the actual. Proceedings of 37th Conference on Decision and Control 1998; 1458–1463.
Google Scholar
19 Aeyels D, Peuteman J. On exponential stability of non-linear time-varying differential equations. Automatica 1999; 35: 1091–1100.
10.1016/S0005-1098(99)00012-6
Web of Science® Google Scholar
20 Hàjek O. Control Theory in the Plane, Springer: Berlin, 1991.
10.1007/BFb0042035
Google Scholar
21 Hahn W. Stability of Motion, Springer: Berlin, 1967.
10.1007/978-3-642-50085-5
Google Scholar
22 Lin Z, Saberi A. Semi-global exponential stabilization of linear systems subject to “input saturation” via linear feedbacks. Systems and Control Letters 1993; 21(3): 225–239.
10.1016/0167-6911(93)90033-3
Web of Science® Google Scholar
23 Schmitendorf WE, Barmish BR. Null controllability of linear systems with constrained controls. SIAM Journal on Control and Optimization 1980; 18: 327–345.
10.1137/0318025
Web of Science® Google Scholar
24 Sontag ED. An algebraic approach to bounded controllability of linear systems. International Journal of Control 1984; 39: 181–188.
10.1080/00207178408933158
Web of Science® Google Scholar

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Volume10, Issue5

Special Issue:Output Regulation for Nonlinear Systems

30 April 2000

Pages 423-438

Output regulation for linear systems with anti-stable eigenvalues in the presence of input saturation

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Output regulation for linear systems with anti-stable eigenvalues in the presence of input saturation

Abstract

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