Guaranteed Cost Finite-Time Control of Fractional-Order Nonlinear Positive Switched Systems with D-Perturbations via MDADT

Liu, Leipo; Cao, Xiangyang; Fu, Zhumu; Song, Shuzhong; Xing, Hao

doi:10.1007/s11424-018-7347-x

Cited by 20 publications

(13 citation statements)

References 17 publications

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“…The ADT and MDADT are well-used tools to cope with switched systems’ analyses and syntheses [ 15 , 36 ]. Since only communication topology switches for the MASs, i.e.…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

“…It considers the joint effect of consensus regulation performance and energy consumption of the control efforts. Thus system performance degradation incurred by the uncertainties or time delays is guaranteed to be less than a derived lower bound [ 15 ]. Some results about the guaranteed cost consensus of MASs have been reported in [ 6 , 28 , 30 ].…”

Section: Introductionmentioning

confidence: 99%

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Guaranteed cost positive consensus for multi-agent systems with multiple time-varying delays and MDADT switching

et al. 2022

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This paper investigates the guaranteed cost positive consensus for linear multi-agent systems (MASs) with multiple time-varying delays and switching topologies. First, necessary and sufficient conditions for the positivity of the focused system are given. The positive consensus criterion and switching signals are derived by combining multiple Lyapunov–Krasovskii functionals with mode-dependent average dwell time approaches. Then, the guaranteed cost positive consensus is studied via the state errors among neighbouring agents and control inputs. It realizes a trade-off between the consensus regulation performance and the control energy consumption of MASs. Particularly, the determined upper bound of the cost function depends merely on the initial conditions of the agents and is independent of the switching movements. Finally, simulation results are given to validate the proposed control scheme.

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“…The ADT and MDADT are well-used tools to cope with switched systems’ analyses and syntheses [ 15 , 36 ]. Since only communication topology switches for the MASs, i.e.…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Guaranteed cost positive consensus for multi-agent systems with multiple time-varying delays and MDADT switching

et al. 2022

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“…Compared with asymptotical stability above, a few results about finite-time stability (FTS) have been presented to study dynamical behaviors of the systems in a finite interval (Liang et al, 2019a;Liu et al, 2019a;Yang and Chen, 2015;Zhang et al, 2016). In Zhang et al (2016), FTS of fractionalorder positive switched systems has been investigated via using the linear copositive Lyapunov function with average dwell time (ADT) technique.…”

Section: Introductionmentioning

confidence: 99%

“…In Zhang et al (2016), FTS of fractionalorder positive switched systems has been investigated via using the linear copositive Lyapunov function with average dwell time (ADT) technique. The problem of guaranteed cost finite-time control of fractional-order nonlinear positive switched systems with D-perturbation has been considered by Liu et al (2019a), and a cost function has been proposed to make full use of positivity of such systems. Yang and Chen (2015) have discussed the FTS analysis of fractional-order positive impulsive switched systems.…”

Section: Introductionmentioning

confidence: 99%

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

Shang

Liu

et al. 2021

Transactions of the Institute of Measurement and Control

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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.

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“…The stability under arbitrary switching is investigated in by employing CLF [15,16] and MLF [17] method. Some other approaches including state-dependent switching [18], ADT [19,20,21] and mode-dependent ADT [22,23] are also adopted. In [24], the formulas of solutions are provided to deal with finite-time stability of FSSs, [25,26] investigate stability of impulsive FSSs including unstable and stable subsystems by utilizing MLF approach and dwell time technique.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Fractional Switched Systems With Stable and Unstable Subsystems

Yang

Liu

et al. 2021

Preprint

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This article addresses stability of fractional switched systems (FSSs) with stable and unstable subsystems. First, several algebraic conditions are presented to guarantee asymptotic stability by applying multiple Lyapunov function (MLF) method, dwell time technique and fast-slow switching mechanism. Then, some stability conditions which have less conservation are also provided by utilizing average dwell time (ADT) technique and the property of Mittag-Leffler function. In addition, sufficient conditions on asymptotic stability of delayed FSSs are obtained by virtue of fractional Razumikhin technique. Finally, several examples are given to reveal that the conclusions obtained are valid.

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Guaranteed Cost Finite-Time Control of Fractional-Order Nonlinear Positive Switched Systems with D-Perturbations via MDADT

Cited by 20 publications

References 17 publications

Guaranteed cost positive consensus for multi-agent systems with multiple time-varying delays and MDADT switching

Guaranteed cost positive consensus for multi-agent systems with multiple time-varying delays and MDADT switching

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

Stability Analysis of Fractional Switched Systems With Stable and Unstable Subsystems

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