| Title:
             | 
Robust exponential stability of a class of nonlinear systems (English) | 
| Author:
             | 
Veselý, Vojtech | 
| Author:
             | 
Rosinová, Danica | 
| Language:
             | 
English | 
| Journal:
             | 
Kybernetika | 
| ISSN:
             | 
0023-5954 | 
| Volume:
             | 
34 | 
| Issue:
             | 
5 | 
| Year:
             | 
1998 | 
| Pages:
             | 
[579]-594 | 
| Summary lang:
             | 
English | 
| . | 
| Category:
             | 
math | 
| . | 
| Summary:
             | 
The paper addresses the problem of design of a robust controller for a class of nonlinear uncertain systems to guarantee the prescribed decay rate of exponential stability. The bounded deterministic uncertainties are considered both in a studied system and its input part. The proposed approach does not employ matching conditions. (English) | 
| Keyword:
             | 
robust exponential stability | 
| Keyword:
             | 
deterministic uncertainties | 
| Keyword:
             | 
nonlinear system | 
| Keyword:
             | 
system design | 
| Keyword:
             | 
robust controller | 
| MSC:
             | 
93B51 | 
| MSC:
             | 
93D09 | 
| MSC:
             | 
93D20 | 
| idZBL:
             | 
Zbl 1274.93223 | 
| idMR:
             | 
MR1663744 | 
| . | 
| Date available:
             | 
2009-09-24T19:20:47Z | 
| Last updated:
             | 
2015-03-28 | 
| Stable URL:
             | 
http://hdl.handle.net/10338.dmlcz/135245 | 
| . | 
| Reference:
             | 
[2] Brogliato B., Neto A. T.: Practical stabilization of a class of nonlinear systems with partially known uncertainties.Automatica 31, (1995), 1, 145–150 Zbl 0825.93650, MR 1312210, 10.1016/0005-1098(94)E0050-R | 
| Reference:
             | 
[3] Chua L. Q., Wu C. W., Huang A., Zhong G. Q.: A universal circuit for studying and generating chaos.Part 1. IEEE Trans. Circuits and Systems (1993), 10, 732–744 Zbl 0844.58053, MR 1255706 | 
| Reference:
             | 
[4] Corles M.: Control of uncertain nonlinear systems.ASME J. Dyn. Syst. Meas. Control 115 (1993), 362–372 10.1115/1.2899076 | 
| Reference:
             | 
[5] Dubrov A. M., Zuber I. E.: Design of exponentially stable control systems for a range of nonlinear processes.Automat. Remote Control (1989), 8, 33–40 MR 1019864 | 
| Reference:
             | 
[6] Fradkov A. L., Pogromsky A. Yu., Markov A. Yu.: Adaptive control of chaotic continuously–time systems.In: Proc. 3rd EC Conference, Roma 1995, pp. 3062–3067 | 
| Reference:
             | 
[7] Gaiduk A. R.: Analytical controller design for a class of nonlinear systems.Automat. Remote Control (1993), 3, 22–33 | 
| Reference:
             | 
[8] Gaiduk A. R.: Analytical nonlinear control systems design.In: Proc. 3rd EC Conference, Roma 1995, pp. 1503–1505 | 
| Reference:
             | 
[9] Jury E. I.: Robustness of discrete systems: A review.In: Proc. 11th IFAC World Congres, Tallin 1990, pp. 184–186 MR 1071016 | 
| Reference:
             | 
[10] Konstantopoulos I. K., Antsaklis P. J.: New bounds for robust stability of continuous and discrete–time systems under parametric uncertainty.Kybernetika 31 (1995), 6, 623–636 Zbl 0872.93065, MR 1374150 | 
| Reference:
             | 
[11] Kozák Š.: Simple and robust PID controller.Appl. Math. Comput. 70 (1995), 2–8 10.1016/0096-3003(94)00119-O | 
| Reference:
             | 
[13] Kučera V., DeSouza C. E.: A necessary and sufficient conditions for output feedback stabilizability.Automatica 31 (1995), 1357–1359 MR 1349414, 10.1016/0005-1098(95)00048-2 | 
| Reference:
             | 
[14] Leitman G.: One method for robust control of uncertain systems: Theory and practice.Kybernetika 32 (1996), 1, 43–62 MR 1380197 | 
| Reference:
             | 
[15] Niculescu S. I., DeSouza C. E., Dugard L., Dion J. M.: Robust exponential stability of uncertain systems with time–varying delays.In: Proc. 3rd EC Conference, Roma 1995, pp. 1802–1807 | 
| Reference:
             | 
[16] Poolla K. S., Shamma J. S., Wise K. A.: Linear and nonlinear controller for robust stabilization problem: A survey.In: Proc. 11th IFAC World Congres, Tallin 1990, pp. 176–183 | 
| Reference:
             | 
[17] Prokop P., Corriou J. P.: Design and analysis of simple robust controllers.Internat. J. Control 66 (1997), 6, 905–921 Zbl 0875.93137, MR 1686734, 10.1080/002071797224450 | 
| Reference:
             | 
[18] Gong, Zhiming, Wen, Changyun, Mital, Dinesh P.: Decentralized robust controller design for a class of interconnected uncertain systems: with known or unknown bound of uncertainty.In: Proc. 3rd EC Conference, Roma 1995, pp. 2940–2945 MR 1391781 | 
| Reference:
             | 
[19] Qu, Zhihua, Dorsey J.: Robust control by two Lyapunov functions.Internat J. Control 55 (1992), 1335–1350 Zbl 0751.93019, MR 1170046, 10.1080/00207179208934288 | 
| Reference:
             | 
[20] Qu, Zhihua: Asymptotic stability of controlling uncertain dynamical systems.Internat. J. Control 59 (1994), 1345–1355 Zbl 0806.93044, MR 1277266, 10.1080/00207179408923134 | 
| . |