Discontinuous piecewise quadratic Lyapunov functions for planar piecewise affine systems

被引：20

作者：

Eghbal, Najmeh ^{[1
]}

Pariz, Naser ^{[1
]}

Karimpour, Ali ^{[1
]}

机构：

[1] Ferdowsi Univ Mashhad, Dept Elect Engn, Mashhad, Iran

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 399卷 / 02期

关键词：

Discontinuous Lyapunov functions; Piecewise affine systems; Stability analysis; DYNAMICAL-SYSTEMS; STABILITY;

D O I：

10.1016/j.jmaa.2012.09.054

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For planar piecewise affine systems, this paper proposes sufficient stability conditions based on discontinuous Lyapunov functions. The monotonicity condition for discontinuous functions at switching instants is presented based on the behavior of state trajectories on the switching surfaces. First, the stability conditions are derived for a typical multiple Lyapunov function and then these conditions are formulated as a set of linear matrix inequalities for piecewise quadratic Lyapunov functions. The implementation of the proposed method is illustrated by an example. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：586 / 593

页数：8

共 20 条

[1]

[Anonymous], 2011, CVX MATLAB SOFTWARE

[2]

[Anonymous], 2003, PIECEWISE LINEAR CON

[3] Efficient conversion of mixed logical dynamical systems into an equivalent piecewise affine form [J].

Bemporad, A .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2004, 49 (05) :832-838

[4] Passivity analysis and passification of discrete-time hybrid systems [J].

Bemporad, Alberto ;

Bianchini, Gianni ;

Brogi, Filippo .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2008, 53 (04) :1004-1009

[5] Complexity of stability and controllability of elementary hybrid systems [J].

Blondel, VD ;

Tsitsiklis, JN .

AUTOMATICA, 1999, 35 (03) :479-489

[6] Multiple Lyapunov functions and other analysis tools for switched and hybrid systems [J].

Branicky, MS .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1998, 43 (04) :475-482

[7] Uniform modeling of parameter dependent nonlinear systems [J].

Eghbal, Najmeh ;

Pariz, Naser ;

Karimpour, Ali .

JOURNAL OF ZHEJIANG UNIVERSITY-SCIENCE C-COMPUTERS & ELECTRONICS, 2012, 13 (11) :850-858

[8] EXISTENCE OF PIECEWISE LINEAR LYAPUNOV FUNCTIONS IN ARBITRARY DIMENSIONS [J].

Giesl, Peter ;

Hafstein, Sigurdur .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2012, 32 (10) :3539-3565

[9]

Hassibi A., 1998, IEEE AM CONTR C PHIL

[10] Equivalence of hybrid dynamical models [J].

Heemels, WPMH ;

De Schutter, B ;

Bemporad, A .

AUTOMATICA, 2001, 37 (07) :1085-1091

← 1 2 →