Finite-Time Control of Uncertain Fractional-Order Positive Impulsive Switched Systems with Mode-Dependent Average Dwell Time

2018 ◽  
Vol 37 (9) ◽  
pp. 3739-3755 ◽  
Author(s):  
Leipo Liu ◽  
Xiangyang Cao ◽  
Zhumu Fu ◽  
Shuzhong Song ◽  
Hao Xing
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Switched Systems ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Time Control ◽  
Impulsive Switched Systems

scholarly journals Nonfragile observer-based guaranteed cost finite-time control of discrete-time positive impulsive switched systems

2019 ◽  
Vol 17 (1) ◽  
pp. 716-727
Author(s):  
Leipo Liu ◽  
Hao Xing ◽  
Xiangyang Cao ◽  
Xiushan Cai ◽  
Zhumu Fu
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Actual State ◽  
Time Control ◽  
Guaranteed Cost ◽  
Impulsive Switched Systems ◽  
Positive Observer

Abstract This paper considers the nonfragile observer-based guaranteed cost finite-time control of discrete-time positive impulsive switched systems(DPISS). Firstly, the positive observer and nonfragile positive observer are designed to estimate the actual state of the underlying systems, respectively. Secondly, by using the average dwell time(ADT) approach and multiple linear co-positive Lyapunov function (MLCLF), two guaranteed cost finite-time controller are designed and sufficient conditions are obtained to guarantee the corresponding closed-loop systems are guaranteed cost finite-time stability(GCFTS). Such conditions can be solved by linear programming. Finally, a numerical example is provided to show the effectiveness of the proposed method.

scholarly journals Guaranteed Cost Finite-Time Control of Discrete-Time Positive Impulsive Switched Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Leipo Liu ◽  
Hao Xing ◽  
Xiangyang Cao ◽  
Zhumu Fu ◽  
Shuzhong Song
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Time Control ◽  
Guaranteed Cost ◽  
Impulsive Switched Systems ◽  
Finite Time Boundedness ◽  
Definition Of

This paper considers the guaranteed cost finite-time boundedness of discrete-time positive impulsive switched systems. Firstly, the definition of guaranteed cost finite-time boundedness is introduced. By using the multiple linear copositive Lyapunov function (MLCLF) and average dwell time (ADT) approach, a state feedback controller is designed and sufficient conditions are obtained to guarantee that the corresponding closed-loop system is guaranteed cost finite-time boundedness (GCFTB). Such conditions can be solved by linear programming. Finally, a numerical example is provided to show the effectiveness of the proposed method.

scholarly journals Guaranteed Cost Finite-Time Control of Fractional-Order Positive Switched Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Leipo Liu ◽  
Xiangyang Cao ◽  
Zhumu Fu ◽  
Shuzhong Song
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Feedback Controller ◽  
Closed Loop Systems ◽  
Time Control ◽  
Guaranteed Cost ◽  
Positive Switched Systems

The problem of guaranteed cost finite-time control of fractional-order positive switched systems (FOPSS) is considered in this paper. Firstly, a new cost function is defined. Then, by constructing linear copositive Lyapunov functions and using the average dwell time (ADT) approach, a state feedback controller and a static output feedback controller are constructed, respectively, and sufficient conditions are derived to guarantee that the corresponding closed-loop systems are guaranteed cost finite-time stable (GCFTS). Such conditions can be easily solved by linear programming. Finally, two examples are given to illustrate 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.

Guaranteed cost and finite-time event-triggered control of fractional-order switched systems

2021 ◽  
pp. 014233122110048
Author(s):  
Yilin Shang ◽  
Leipo Liu ◽  
Yifan Di ◽  
Zhumu Fu ◽  
Bo Fan
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Electrical Circuit ◽  
Linear Matrix ◽  
Current State ◽  
Guaranteed Cost ◽  
Event Triggered

This paper considers the problem of guaranteed cost and finite-time event-triggered control of fractional-order switched systems. Firstly, an event-triggered scheme including both the information of current state and an exponential decay function is proposed, and a novel cost function that adopts the characteristics of fractional-order integration is presented. Secondly, some sufficient conditions are derived to guarantee that the corresponding closed-loop system is finite-time stable with a certain cost upper bound, using multiple Lyapunov functions and average dwell time approach. Meanwhile, the event-triggered parameters and state feedback gains are simultaneously obtained via solving linear matrix inequalities. Moreover, Zeno behavior does not exist by finding a positive lower bound of the triggered interval. Finally, an example about fractional-order switched electrical circuit is provided to show the effectiveness of the proposed method.

Observer-based H∞ finite-time control for switched linear systems with interval time-delay

2018 ◽  
Vol 41 (5) ◽  
pp. 1348-1360 ◽  
Author(s):  
Gökhan Göksu ◽  
Ulviye Başer
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Linearization Method ◽  
Interval Time ◽  
Time Control ◽  
Finite Time Boundedness ◽  
Time Bounds

In this work, interval time-delay switched systems having completely unstable and mixed stable matrices of the state vector are considered. An observer-based controller is designed for finite-time boundedness and H∞-control of these systems. New sufficient conditions on the existence of a desired observer are developed and new average dwell-time bounds are introduced separately in case of unstable and mixed stable subsystems. An algorithm is presented for the calculation of unknown constants in the average dwell-time bounds which depend on nonlinear matrices in terms of the cone complementarity linearization method. Finally, numerical examples are given for the effectiveness and validity of the proposed solutions.

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