Geodesic
Robust stability of non linear time varying systems
Kybernetika, Tome 35 (1999) no. 4, pp. 415-428 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Systems with time-varying non-linearity confined to a given sector (Luré type) and a linear part with uncertainty formulated by an interval transfer function, are considered. Sufficient conditions satisfying the Popov criterion for stability, which are computationally tractable, are derived. The problem of checking the Popov criterion for an infinite set of systems, is reduced to that of checking the Popov criterion for a finite number of fixed coefficient systems, each in a prescribed frequency interval. Illustrative numerical examples are provided.
Systems with time-varying non-linearity confined to a given sector (Luré type) and a linear part with uncertainty formulated by an interval transfer function, are considered. Sufficient conditions satisfying the Popov criterion for stability, which are computationally tractable, are derived. The problem of checking the Popov criterion for an infinite set of systems, is reduced to that of checking the Popov criterion for a finite number of fixed coefficient systems, each in a prescribed frequency interval. Illustrative numerical examples are provided.
Classification : 93C10, 93D09, 93D10
Keywords: Popov criterion; stability; time-varying nonlinearity; Lur’e type nonlinearity; interval transfer function 
@article{KYB_1999_35_4_a1,
     author = {Zeheb, Ezra},
     title = {Robust stability of non linear time varying systems},
     journal = {Kybernetika},
     pages = {415--428},
     year = {1999},
     volume = {35},
     number = {4},
     mrnumber = {1723522},
     zbl = {1274.93224},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1999_35_4_a1/}
}
TY  - JOUR
AU  - Zeheb, Ezra
TI  - Robust stability of non linear time varying systems
JO  - Kybernetika
PY  - 1999
SP  - 415
EP  - 428
VL  - 35
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/KYB_1999_35_4_a1/
LA  - en
ID  - KYB_1999_35_4_a1
ER  - 
%0 Journal Article
%A Zeheb, Ezra
%T Robust stability of non linear time varying systems
%J Kybernetika
%D 1999
%P 415-428
%V 35
%N 4
%U http://geodesic.mathdoc.fr/item/KYB_1999_35_4_a1/
%G en
%F KYB_1999_35_4_a1
Zeheb, Ezra. Robust stability of non linear time varying systems. Kybernetika, Tome 35 (1999) no. 4, pp. 415-428. http://geodesic.mathdoc.fr/item/KYB_1999_35_4_a1/

[1] Brockett R. W., Lee H. B.: Frequency–domain instability criteria for time–varying and nonlinear systems. Proc. IEEE 55 (1967), 604–618

[2] Fruchter G., Srebro U., Zeheb E.: An analytic method for design of uncertain discrete nonlinear control systems. In: Proc. of the 15th Conference of IEEE in Israel, Tel-Aviv 1987

[3] Fruchter G.: Generalized zero sets location and absolute robust stabilization of continuous nonlinear control systems. Automatica 27 (1991), 501–512 | DOI | MR | Zbl

[4] Fruchter G., Srebro U., Zeheb E.: Stability of discrete nonlinear control systems. IMA J. Math. Control Inform. 14 (1997), 333–351 | DOI | MR | Zbl

[5] Kerbelev A. M.: A circle criterion for robust stability and instability of nonstationary nonlinear systems. Automat. Remote Control 54 (1993), 12, 1820–1823 | MR | Zbl

[6] Kharitonov V. L.: Asymptotic stability of an equilibrium of a family of system of linear differential equations. Differential Equations 14 (1979), 1483–1485

[7] Levkovich A., Zeheb E., Cohen N.: Frequency response envelopes of a family of uncertain continuous–time systems. IEEE Trans. Circuits and Systems 42 (1995), 156–165 | DOI | MR | Zbl

[8] Popov V. M.: Absolute stability of nonlinear systems of automatic control. Translated from Automatika i Telemekhanika 22 (1961), 961–979 | MR | Zbl

[9] Rozenvasser E. N.: The absolute stability of non–linear systems. Translated from Automatika i Telemekhanika 24 (1963), 304–313 | MR

[10] Siljak D.: Parameter analysis of absolute stability. Automatica 5 (1969), 385–387 | DOI | Zbl

[11] Siljak D.: Polytopes of nonnegative polynomials. In: Proc. of the American Control Conf. (ACC), Pittsburgh 1989, pp. 193-199

[12] Zeheb E.: Robust stability of non–linear time varying systems. In: Proc. of the 5th IEEE Mediterranean Conf. on Control and Systems, Paphos 1997