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.

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Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 3

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



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