| Title:
|
Local asymptotic stability for nonlinear state feedback delay systems (English) |
| Author:
|
Germani, Alfredo |
| Author:
|
Manes, Costanzo |
| Author:
|
Pepe, Pierdomenico |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
36 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
[31]-42 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper considers the problem of output control of nonlinear delay systems by means of state delayed feedback. In previous papers, through the use of a suitable formalism, standard output control problems, such as output regulation, trajectory tracking, disturbance decoupling and model matching, have been solved for a class of nonlinear delay systems. However, in general an output control scheme does not guarantee internal stability of the system. Some results on this issue are presented in this paper. It is proved that if the system owns a certain Lipschitz property in a suitable neighborhood of the origin, and the initial state is inside such neighborhood, then when the output is driven to zero by means of a static state feedback the system state asymptotically goes to zero. Theoretical results are supported by computer simulations performed on a nonlinear delay systems that is unstable in open loop. (English) |
| Keyword:
|
nonlinear delay system |
| Keyword:
|
state delayed feedback |
| MSC:
|
93C10 |
| MSC:
|
93C23 |
| MSC:
|
93D05 |
| MSC:
|
93D15 |
| MSC:
|
93D25 |
| idZBL:
|
Zbl 1249.93146 |
| idMR:
|
MR1760886 |
| . |
| Date available:
|
2009-09-24T19:30:43Z |
| Last updated:
|
2015-03-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135332 |
| . |
| Reference:
|
[1] Banks H. T., Kappel F.: Spline approximations for functional differential equations.J. Differential Equations 34 (1979), 496–522 Zbl 0422.34074, MR 0555324, 10.1016/0022-0396(79)90033-0 |
| Reference:
|
[2] Bensoussan A., Prato G. Da, Delfour M. C., Mitter S. K.: Representation and Control of Infinite Dimensional Systems.Birkhäuser, Boston 1992 Zbl 1117.93002, MR 2273323 |
| Reference:
|
[3] Germani A., Manes C., Pepe P.: Numerical solution for optimal regulation of stochastic hereditary systems with multiple discrete delays.In: Proc. of 34th IEEE Conference on Decision and Control, Louisiana 1995. Vol. 2, pp. 1497–1502 |
| Reference:
|
[4] Germani A., Manes C., Pepe P.: Linearization of input–output mapping for nonlinear delay systems via static state feedback.In: Proc. of CESA IMACS Multiconference on Computational Engineering in Systems Applications, Lille 1996, Vol. 1, pp. 599–602 |
| Reference:
|
[5] Germani A., Manes C., Pepe P.: Linearization and decoupling of nonlinear delay systems.In: Proc. of 1998 American Control Conference, ACC’98, Philadelphia 1998, Vol. 3, pp. 1948–1952 |
| Reference:
|
[6] Germani A., Manes C., Pepe P.: Tracking, model matching, disturbance decoupling for a class of nonlinear delay systems.In: Proc. of Large Scale Systems IFAC Conference, LSS’98, Patrasso 1998, Vol. 1, pp. 423–429 |
| Reference:
|
[7] Germani A., Manes C., Pepe P.: A state observer for nonlinear delay systems.In: Proc. of 37th IEEE Conference on Decision and Control, Tampa 1998 |
| Reference:
|
[8] Gibson J. S.: Linear quadratic optimal control of hereditary differential systems: Infinite–dimensional Riccati equations and numerical approximations.SIAM J. Control Optim. 31 (1983), 95–139 Zbl 0557.49017, MR 0688442, 10.1137/0321006 |
| Reference:
|
[9] Isidori A.: Nonlinear Control Systems.Third edition. Springer–Verlag, London 1995 Zbl 0931.93005, MR 1410988 |
| Reference:
|
[10] Lehman B., Bentsman J., Lunel S. V., Verriest E. I.: Vibrational control of nonlinear time lag systems with bounded delay: Averaging theory, stabilizability, and transient behavior.IEEE Trans. Automat. Control 5 (1994), 898–912 Zbl 0813.93044, MR 1274337, 10.1109/9.284867 |
| Reference:
|
[11] Marquez L. A., Moog C. H., Velasco M.: The structure of nonlinear time delay system.In: Proc. of 6th Mediterranean Conference on Control and Automation, Alghero 1998 |
| Reference:
|
[12] Moog C. H., Castro R., Velasco M.: The disturbance decoupling problem for nonlinear systems with multiple time–delays: Static state feedback solutions.In: Proc. of CESA IMACS Multiconference on Computational Engineering in Systems Applications, Vol. 1, pp. 596–598, Lille 1996 |
| Reference:
|
[13] Moog C. H., Castro R., Velasco M.: Bi–causal solutions to the disturbance decoupling problem for time–delay nonlinear systems.In: Proc. of 36th IEEE Conference on Decision and Control, Vol. 2, pp. 1621–1622, San Diego, 1997 |
| Reference:
|
[14] Pandolfi L.: The standard regulator problem for systems with input delays.An approach through singular control theory. Appl. Math. Optim. 31 (1995), 2, 119–136 Zbl 0815.49006, MR 1309302, 10.1007/BF01182784 |
| Reference:
|
[15] Pepe P.: Il Controllo LQG dei Sistemi con Ritardo.PhD Thesis, Department of Electrical Engineering, L’Aquila 1996 |
| Reference:
|
[16] Wu J. W., Hong K.-S.: Delay–independent exponential stability criteria for time–varying discrete delay systems.IEEE Trans. Automat. Control 39 (1994), 4, 811–814 Zbl 0807.93055, MR 1276779, 10.1109/9.286258 |
| . |
