State feedback stabilization of a class of uncertain nonlinear systems on non-uniform time domains

被引：29

作者：

Ben Nasser, Bacem ^{[1
]}

Boukerrioua, Khaled ^{[2
]}

Defoort, Michael ^{[3
]}

Djemai, Mohamed ^{[3
]}

Hammami, Mohamed Ali ^{[1
]}

机构：

[1] Univ Sfax, Fac Sci Sfax, Dept Math, POB 802, Sfax 3038, Tunisia

[2] Univ May 8, Fac Math Informat & Mat Sci, Dept Math, 1945 Guelma,POB 401, Guelma 24000, Algeria

[3] UVHC, CNRS, UMR 8201, LAMIH, F-59313 Le Mt Houy, Valenciennes, France

来源：

SYSTEMS & CONTROL LETTERS | 2016年 / 97卷

关键词：

Time scales; Stabilization; Nonlinear systems; Exponential stability; Practical stability; LINEAR-CONTROL SYSTEMS; DYNAMIC EQUATIONS; EXPONENTIAL STABILITY; REALIZATIONS; MATRIX;

D O I：

10.1016/j.sysconle.2016.08.005

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper deals with the stabilization problem for a class of uncertain nonlinear systems on non-uniform time domains. Some sufficient conditions are derived to design a state feedback controller for a class of uncertain nonlinear time-varying systems under vanishing perturbations. Using some Gronwall's integral inequalities, the uniform exponential stability of the closed-loop systems on arbitrary time scales, is guaranteed. Then, based on the Lyapunov theory, new sufficient conditions are proposed to derive the controller which ensures the practical stability of the closed-loop time-invariant nonlinear uncertain system under non-vanishing perturbations. Some examples illustrate these results. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：18 / 26

页数：9

共 40 条

[21] Transition matrix and generalized matrix exponential via the Peano-Baker series [J].

Dacunha, JJ .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2005, 11 (15) :1245-1264

[22] Stability for time varying linear dynamic systems on time scales [J].

DaCunha, JJ .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 176 (02) :381-410

[23]

Davis John M., 2010, 2010 42nd Southeastern Symposium on System Theory (SSST 2010), P9, DOI 10.1109/SSST.2010.5442794

[24] Stability radii for positive linear time-invariant systems on time scales [J].

Doan, T. S. ;

Kalauch, A. ;

Siegmund, S. ;

Wirth, F. R. .

SYSTEMS & CONTROL LETTERS, 2010, 59 (3-4) :173-179

[25] On the exponential stability of dynamic equations on time scales [J].

Du, Nguyen Huu ;

Tien, Le Huy .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 331 (02) :1159-1174

[26]

Fausett L.V., 2004, NONLINEAR STUD, V11, P627

[27]

Hamza A. E., 2013, INT J CONT MATH SCI, V8, P469, DOI [https://doi.org/10.12988/ijcms.2013.13047, DOI 10.12988/IJCMS.2013.13047]

[28] Linear state feedback stabilisation on time scales [J].

Jackson, Billy J. ;

Davis, John M. ;

Gravagne, Ian A. ;

Marks, Robert J., II .

INTERNATIONAL JOURNAL OF DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS, 2011, 3 (1-2) :163-177

[29] Explicit bounds on some new nonlinear integral inequalities with delay [J].

Jiang, Fangcui ;

Meng, Fanwei .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 205 (01) :479-486

[30] Lyapunov functions for linear nonautonomous dynamical equations on time scales [J].

Kloeden, Peter E. ;

Zmorzynska, Alexandra .

ADVANCES IN DIFFERENCE EQUATIONS, 2006, 2006 (1)

← 1 2 3 4 →