Piecewise-quadratic Lyapunov functions for systems with deadzones or saturations

被引：68

作者：

Dai, Dan ^{[2
]}

Hu, Tingshu ^{[3
]}

Teel, Andrew R. ^{[2
]}

Zaccarian, Luca ^{[1
]}

机构：

[1] Univ Rome, Dipartimento Informat, I-00133 Rome, Italy

[2] Univ Calif Santa Barbara, Dept Elect & Comp Engn, Santa Barbara, CA 93106 USA

[3] Univ Massachusetts, Dept Elect & Comp Engn, Lowell, MA 01854 USA

来源：

SYSTEMS & CONTROL LETTERS | 2009年 / 58卷 / 05期

关键词：

Piecewise quadratic Lyapunov function; Saturation; Deadzone; Nonlinear L-2 gain; Reachable set; Domain of attraction; LMIs; CONTROLLER SYNTHESIS; INPUT SATURATION; LINEAR-SYSTEMS; ANTIWINDUP; STABILITY;

D O I：

10.1016/j.sysconle.2009.01.003

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A piecewise quadratic Lyapunov function is developed for the analysis of the global and regional performances for systems with saturation/deadzone in a general feedback configuration with an algebraic loop. This piecewise quadratic Lyapunov function effectively incorporates the structure of the saturation/dead zone nonlinearity. Several sector-like conditions are derived to describe the complex nonlinear algebraic loop. These conditions transform several performance analysis problems into optimization problems with linear (or bilinear) matrix inequalities. The effectiveness of the results is demonstrated with numerical examples. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：365 / 371

页数：7

共 21 条

[1] The explicit linear quadratic regulator for constrained systems [J].

Bemporad, A ;

Morari, M ;

Dua, V ;

Pistikopoulos, EN .

AUTOMATICA, 2002, 38 (01) :3-20

[2] An antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation [J].

Cao, YY ;

Lin, ZL ;

Ward, DG .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2002, 47 (01) :140-145

[3]

da Silva JMG, 2002, PROCEEDINGS OF THE 2002 IEEE INTERNATIONAL CONFERENCE ON CONTROL APPLICATIONS, VOLS 1 & 2, P1106, DOI 10.1109/CCA.2002.1038759

[4] Antiwindup design with guaranteed regions of stability: An LMI-based approach [J].

da Silva, JMG ;

Tarbouriech, S .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2005, 50 (01) :106-111

[5]

Gonçalves JM, 2001, P AMER CONTR CONF, P4183, DOI 10.1109/ACC.2001.945632

[6] Antiwindup for stable linear systems with input saturation: An LMI-based synthesis [J].

Grimm, G ;

Hatfield, J ;

Postlethwaite, I ;

Teel, AR ;

Turner, MC ;

Zaccarian, L .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2003, 48 (09) :1509-1525

[7]

Haddad WM, 1997, INT J ROBUST NONLIN, V7, P675, DOI 10.1002/(SICI)1099-1239(199711)7:7<675::AID-RNC217>3.0.CO

[8]

2-G

[9] EXPLICIT CONSTRUCTION OF QUADRATIC LYAPUNOV FUNCTIONS FOR THE SMALL GAIN, POSITIVITY, CIRCLE, AND POPOV THEOREMS AND THEIR APPLICATION TO ROBUST STABILITY .1. CONTINUOUS-TIME THEORY [J].

HADDAD, WM ;

BERNSTEIN, DS .

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 1993, 3 (04) :313-339

[10] Anti-windup synthesis for linear control systems with input saturation: Achieving regional, nonlinear performance [J].

Hu, Tingshu ;

Teel, Andrew R. ;

Zaccarian, Luca .

AUTOMATICA, 2008, 44 (02) :512-519

← 1 2 3 →