Technical Brief

Positive Finite-Time Stabilization for Discrete-Time Linear Systems

[+] Author and Article Information
Wenping Xue

School of Electrical and Information Engineering,
Jiangsu University,
Zhenjiang 212013, China
e-mail: xwping@ujs.edu.cn

Kangji Li

School of Electrical and Information Engineering,
Jiangsu University,
Zhenjiang 212013, China
e-mail: likangji@ujs.edu.cn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 5, 2013; final manuscript received July 28, 2014; published online August 28, 2014. Assoc. Editor: Qingze Zou.

J. Dyn. Sys., Meas., Control 137(1), 014502 (Aug 28, 2014) (5 pages) Paper No: DS-13-1100; doi: 10.1115/1.4028141 History: Received March 05, 2013; Revised July 28, 2014

In this paper, a new finite-time stability (FTS) concept, which is defined as positive FTS (PFTS), is introduced into discrete-time linear systems. Differently from previous FTS-related papers, the initial state as well as the state trajectory is required to be in the non-negative orthant of the Euclidean space. Some test criteria are established for the PFTS of the unforced system. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is positively finite-time stable. This condition is provided in terms of a series of linear matrix inequalities (LMIs) with some equality constraints. Moreover, the requirement of non-negativity of the controller is considered. Finally, two examples are presented to illustrate the developed theory.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Fig. 1

err(c2) introduced by the sufficient condition in Theorem 2

Grahic Jump Location
Fig. 2

Closed-loop weighted state norm from four different initial conditions for Example 1

Grahic Jump Location
Fig. 3

Closed-loop system from Example 2: state responses and ‖x∧‖R (top) as well as the control input (bottom)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In