W-Stability of Multistable Nonlinear Discrete-Time Systems

被引：0

作者：

Ding, Zhishuai ^{[1
]}

Cheng, Guifang ^{[1
,2
]}

Mu, Xiaowu ^{[1
]}

机构：

[1] Zhengzhou Univ, Dept Math, Zhengzhou 450001, Hennan, Peoples R China

[2] Zhengzhou Univ, Phys Engn Coll, Zhengzhou 450001, Hennan, Peoples R China

来源：

DISCRETE DYNAMICS IN NATURE AND SOCIETY | 2012年 / 2012卷

关键词：

CONVERSE LYAPUNOV THEOREM; FEEDBACK;

D O I：

10.1155/2012/418091

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization formultistable discrete-time nonlinear systems. Based on a new type stability notion of W-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.

引用

页数：11

共 22 条

[1]

Agarwal R.P., 1992, Monographs and Textbooks in Pure and Applied Mathematics, V155

[2] Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feed back systems [J].

Angeli, D ;

Ferrell, JE ;

Sontag, ED .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2004, 101 (07) :1822-1827

[3] Oscillations in I/O monotone systems under negative feedback [J].

Angeli, David ;

Sontag, Eduardo D. .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2008, 53 :166-176

[4] Allee effect in a discrete-time predator-prey system [J].

Celik, Canan ;

Duman, Oktay .

CHAOS SOLITONS & FRACTALS, 2009, 40 (04) :1956-1962

[5] The permanence and global attractivity of Lotka-Volterra competition system with feedback controls [J].

Chen, FD .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2006, 7 (01) :133-143

[6] Finite-time stability with respect to a closed invariant set for a class of discontinuous systems [J].

Cheng, Gui-fang ;

Mu, Xiao-wu .

APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 2009, 30 (08) :1069-1075

[7] On global Lyapunov characterization of multi-stable nonlinear systems [J].

Efimov, Denis .

PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009), 2009, :6299-6304

[8] Monotone systems under positive feedback: multistability and a reduction theorem [J].

Enciso, G ;

Sontag, ED .

SYSTEMS & CONTROL LETTERS, 2005, 54 (02) :159-168

[9] Input-to-state stability for discrete-time nonlinear systems [J].

Jiang, ZP ;

Wang, Y .

AUTOMATICA, 2001, 37 (06) :857-869

[10] A converse Lyapunov theorem for discrete-time systems with disturbances [J].

Jiang, ZP ;

Wang, Y .

SYSTEMS & CONTROL LETTERS, 2002, 45 (01) :49-58

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