Robust Finite-Time Stability of Fractional Order Linear Time-Varying Impulsive Systems

2014 ◽  
Vol 34 (4) ◽  
pp. 1325-1341 ◽  
Author(s):  
Guopei Chen ◽  
Ying Yang
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Linear Time ◽  
Time Varying ◽  
Impulsive Systems ◽  
Time Stability ◽  
Order Linear ◽  
Finite Time Stability

scholarly journals Finite-time stability analysis for linear time-varying singular impulsive systems

2011 ◽  
Vol 6 (16) ◽  
pp. 3344-3350
Author(s):  
Zhou Linna ◽  
Yang Chunyu ◽  
Zhang Qingling ◽  
Lai Yingwu
Keyword(s):  
Stability Analysis ◽  
Finite Time ◽  
Linear Time ◽  
Time Varying ◽  
Impulsive Systems ◽  
Time Stability ◽  
Finite Time Stability

Input–output finite time stability of fractional order linear systems with 0 < α < 1

2015 ◽  
Vol 39 (5) ◽  
pp. 653-659 ◽  
Author(s):  
Ya-jing Ma ◽  
Bao-wei Wu ◽  
Yue-E Wang ◽  
Ye Cao
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Linear Time ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Input Output ◽  
Time Stability ◽  
Caputo Fractional Derivatives ◽  
Order Linear ◽  
Finite Time Stability

The input–output finite time stability (IO-FTS) for a class of fractional order linear time-invariant systems with a fractional commensurate order 0 < α < 1 is addressed in this paper. In order to give the stability property, we first provide a new property for Caputo fractional derivatives of the Lyapunov function, which plays an important role in the main results. Then, the concepts of the IO-FTS for fractional order normal systems and fractional order singular systems are introduced, and some sufficient conditions are established to guarantee the IO-FTS for fractional order normal systems and fractional order singular systems, respectively. Finally, the state feedback controllers are designed to maintain the IO-FTS of the resultant fractional order closed-loop systems. Two numerical examples are provided to illustrate the effectiveness of the proposed results.

scholarly journals FTS and FTB of Conformable Fractional Order Linear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Abdellatif Ben Makhlouf ◽  
Omar Naifar ◽  
Mohamed Ali Hammami ◽  
Bao-wei Wu
Keyword(s):  
Fractional Derivative ◽  
Linear Systems ◽  
Fractional Order ◽  
Finite Time ◽  
Conformable Fractional Derivative ◽  
Time Stability ◽  
Order Linear ◽  
Finite Time Stability ◽  
Finite Time Boundedness

In this paper, an extension of some existing results related to finite-time stability (FTS) and finite-time boundedness (FTB) into the conformable fractional derivative is presented. Illustrative example is presented at the end of the paper to show the effectiveness of the proposed result.

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