Input–Output Finite-Time Stability of Fractional-Order Positive Switched Systems

2018 ◽  
Vol 38 (4) ◽  
pp. 1619-1638 ◽  
Author(s):  
Jinxia Liang ◽  
Baowei Wu ◽  
Yue-E Wang ◽  
Ben Niu ◽  
Xuejun Xie
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Switched Systems ◽  
Input Output ◽  
Time Stability ◽  
Finite Time Stability ◽  
Positive Switched Systems

Finite-time stability and finite-time boundedness of fractional order switched systems

2019 ◽  
Vol 41 (12) ◽  
pp. 3364-3371 ◽  
Author(s):  
Jinxia Liang ◽  
Baowei Wu ◽  
Lili Liu ◽  
Yue-E Wang ◽  
Changtao Li
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Boundedness

Finite-time stability and finite-time boundedness of fractional order switched systems with [Formula: see text] are investigated in this paper. First of all, by employing the average dwell time technique and Lyapunov functional method, some sufficient conditions for finite-time stability and finite-time boundedness of fractional order switched systems are proposed. Furthermore, the state feedback controllers are constructed, and sufficient conditions are given to ensure that the corresponding closed-loop systems are finite-time stable and finite-time bounded. These conditions can be easily obtained in terms of linear matrix inequalities. Finally, two numerical examples are given to show the effectiveness of the results.

scholarly journals Input-Output Finite-Time Control of Positive Switched Systems with Time-Varying and Distributed Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Leipo Liu ◽  
Xiangyang Cao ◽  
Zhumu Fu ◽  
Shuzhong Song
Keyword(s):  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Distributed Delays ◽  
Time Varying ◽  
Input Output ◽  
Finite Time Stability ◽  
Time Control ◽  
Positive Switched Systems

The problem of input-output finite-time control of positive switched systems with time-varying and distributed delays is considered in this paper. Firstly, the definition of input-output finite-time stability is extended to positive switched systems with time-varying and distributed delays, and the proof of the positivity of such systems is also given. Then, by constructing multiple linear copositive Lyapunov functions and using the mode-dependent average dwell time (MDADT) approach, a state feedback controller is designed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is input-output finite-time stable (IO-FTS). Such conditions can be easily solved by linear programming. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

Asynchronously input-output finite-time control of discrete-time nonlinear impulsive positive switched systems

2019 ◽  
Vol 41 (14) ◽  
pp. 4157-4166 ◽  
Author(s):  
Leipo Liu ◽  
Hao Xing ◽  
Xiangyang Cao ◽  
Zhumu Fu ◽  
Yifan Di
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Switched Systems ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Input Output ◽  
Finite Time Stability ◽  
Time Control ◽  
Positive Switched Systems

This paper considers asynchronously input-output finite-time control of discrete-time nonlinear impulsive positive switched systems (DNIPSS). Firstly, the definition of input-output finite-time stability (IO-FTS) is introduced. By using the linear co-positive Lyapunov function (LCLF) and average dwell time (ADT) approach, a state feedback controller via asynchronous switching is designed and sufficient conditions are obtained to guarantee the corresponding closed-loop system is IO-FTS. Such conditions can be solved by linear programming. Furthermore, the mode-dependent average dwell time (MDADT) method for asynchronously input-output finite-time control of DNIPSS is also presented. Finally, two examples are provided to show the effectiveness of the proposed method.

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.

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