Multi-rate sampled-data composite control of linear singularly perturbed systems

被引：16

作者：

Chen, Wu-Hua ^{[1
]}

He, Haohua ^{[2
]}

Lu, Xiaomei ^{[2
]}

机构：

[1] Guangxi Univ, Sch Elect Engn, Nanning 530004, Guangxi, Peoples R China

[2] Guangxi Univ, Coll Math & Informat Sci, Nanning 530004, Guangxi, Peoples R China

来源：

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS | 2020年 / 357卷 / 04期

基金：

中国国家自然科学基金;

关键词：

STABILITY ANALYSIS; EXPONENTIAL STABILITY; DIGITAL-CONTROL; DESIGN; STABILIZATION; OBSERVER;

D O I：

10.1016/j.jfranklin.2019.11.037

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 addresses the multi-rate stabilization problem for linear singularly perturbed systems. The proposed multi-rate sampled-data control law is based on the discretization in multi-rate fashion on the continuous-time composite control law obtained from the singular perturbation theory. The sampling times of the slow and fast state variables are allowed to be asynchronous and nonuniformly spaced. A new time-dependent Lyapunov functional is introduced to analyze the closed-loop stability of the considered system with the multi-rate feedback. With the use of the Lyapunov functional, a sufficient condition for exponential stability of the closed-loop system is derived in terms of linear matrix inequalities. Further, a robust stabilizability condition of the proposed multi-rate control law with respect to uncertain singular perturbation parameter is also obtained. Three numerical examples are presented to show the effectiveness of the developed methodology. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

引用

页码：2028 / 2048

页数：21

共 34 条

[1] Event-triggered control of nonlinear singularly perturbed systems based only on the slow dynamics [J].

Abdelrahim, Mahmoud ;

Postoyan, Tcomain ;

Daafouz, Jamal .

AUTOMATICA, 2015, 52 :15-22

[2] Stability analysis of a general class of singularly perturbed linear hybrid systems [J].

Ben Rejeb, Jihene ;

Morarescu, Irinel-Constantin ;

Girard, Antoine ;

Daafouz, Jamal .

AUTOMATICA, 2018, 90 :98-108

[3] A hierarchical controller for miniature VTOL UAVs: Design and stability analysis using singular perturbation theory [J].

Bertrand, Sylvain ;

Guenard, Nicolas ;

Hamel, Tarek ;

Piet-Lahanier, Helene ;

Eck, Laurent .

CONTROL ENGINEERING PRACTICE, 2011, 19 (10) :1099-1108

[4] Event-Triggered Composite Control of a Two Time Scale System [J].

Bhandari, Manisha ;

Fulwani, Deepak M. ;

Gupta, Rajeev .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS, 2018, 65 (04) :471-475

[5] A multirate digital control via a discrete-time observer for non-linear singularly perturbed continuous-time systems [J].

Bidani, M ;

Djemaï, M .

INTERNATIONAL JOURNAL OF CONTROL, 2002, 75 (08) :591-613

[6] Robust sampled-data H∞ control of uncertain singularly perturbed systems using time-dependent Lyapunov functionals [J].

Chen, Wu-Hua ;

Wang, Zipeng ;

Wei, Dan ;

Lu, Xiaomei .

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 2015, 46 (15) :2832-2852

[7] Exponential stability of a class of nonlinear singularly perturbed systems with delayed impulses [J].

Chen, Wu-Hua ;

Wei, Dan ;

Lu, Xiaomei .

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2013, 350 (09) :2678-2709

[8] An Improved Stabilization Method for Sampled-Data Control Systems With Control Packet Loss [J].

Chen, Wu-Hua ;

Zheng, Wei Xing .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2012, 57 (09) :2378-2384

[9] Input-to-state stability for networked control systems via an improved impulsive system approach [J].

Chen, Wu-Hua ;

Zheng, Wei Xing .

AUTOMATICA, 2011, 47 (04) :789-796

[10] Caputo and related fractional derivatives in singular systems [J].

Dassios, Ioannis K. ;

Baleanu, Dumitru, I .

APPLIED MATHEMATICS AND COMPUTATION, 2018, 337 :591-606

← 1 2 3 4 →