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.
Positive Finite-Time Stabilization for Discrete-Time Linear Systems
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.
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Xue, W., and Li, K. (August 28, 2014). "Positive Finite-Time Stabilization for Discrete-Time Linear Systems." ASME. J. Dyn. Sys., Meas., Control. January 2015; 137(1): 014502. https://doi.org/10.1115/1.4028141
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