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.
BorahMSinghPPRoyB. K. (2016) Improved chaotic dynamics of a fractional-order system, its chaos-suppressed synchronisation and circuit implementation. Circuits Systems and Signal Processing35(6): 1871–1907.
2.
ChenYFeiSLiY (2017) Robust stabilization for uncertain saturated time-delay systems: a distributed-delay-dependent polytopic approach. IEEE Transactions on Automatic Control62(7): 3455–3460.
3.
ChenYWangZLiuY, et al. (2018) Stochastic stability for distributed delay neural networks via augmented Lyapunov-Krasovskii functionals. Applied Mathematics and Computation338: 869–881.
4.
ChenYWenGPengZ (2019) Consensus of fractional-order multi-agent system via sampled-data event-triggered control. Journal of the Franklin Institute356(17): 10241–10259.
5.
FengTWuBLiuL, et al. (2019a) Finite-time stability and stabilization of fractional-order switched singular continuous-time systems. Circuits Systems and Signal Processing38(12): 5528–5548.
6.
FengTWuBWangY, et al. (2019b) Input-output finite-time stability of fractional-order switched singular continuous-time systems. Asian Journal of Control38(4): 1619–1638.
7.
HosseinNiaS.H.TejadoInésVinagreB.M. (2013) Stability of fractional order switching systems. Computers and Mathematics with Applications66(5): 585–596.
8.
HuTHeZZhangX, et al. (2020) Leader-following consensus of fractional-order multi-agent systems based on event-triggered control. Nonlinear Dynamics99(3): 2219–2232.
9.
KaczorekT (2016) Minimum energy control of fractional positive electrical circuits with bounded inputs. Circuits, Systems, and Signal Processing35(6): 1815–1829.
10.
LiQLiuSChenY (2018) Combination event-triggered adaptive networked synchronization communication for nonlinear uncertain fractional-order chaotic systems. Applied Mathematics and Computation 333: 521–535.
11.
LiTFuJ (2017) Event-triggered control of switched linear systems. Journal of the Franklin Institute354(15): 6451–6462.
12.
LiangJWuBWangY (2019a) Input-output finite-time stability of fractional-order positive switched systems. Circuits Systems and Signal Processing38(4): 1619–1638.
13.
LiangJWuBWangY, et al. (2019b) Finite-time stability and finite-time boundedness of fractional order switched systems. Transactions of the Institute of Measurement and Control41(12): 3364–3371.
14.
LiuLCaoXFuZ, et al. (2017) Guaranteed cost finite-time control of fractional-order positive switched systems. Advances in Mathematical Physics 2017: 1–11.
15.
LiuLCaoXFuZ, et al. (2018a) Finite-time control of uncertain fractional-order positive impulsive switched systems with mode-dependent average dwell time. Circuits Systems, and Signal Processing37(9): 3739–3755.
16.
LiuLCaoXFuZ, et al. (2018b) Input-output finite-time control of uncertain positive impulsive switched systems with time-varying and distributed delays. International Journal of Control, Automation and Systems16(2): 670–681.
17.
LiuLCaoXFuZ, et al. (2019a) Guaranteed cost finite-time control of fractional-order nonlinear positive switched systems with D-Perturbations via MDADT. Journal of Systems Science and Complexity32(3): 857–874.
18.
LiuLCaoXFuZ, et al. (2019b) Positive impulsive observer design of fractional-order positive switched systems with MDADT. Transactions of the Institute of Measurement and Control41(5): 1340–1347.
19.
LiuLXingHCaoX, et al. (2019c) Asynchronously input-output finite-time control of discrete-time nonlinear impulsive positive switched systems. Transactions of the Institute of Measurement and Control41(14): 4157–4166.
20.
LiuLXingHDiY, et al. (2020) Asynchronously input-output finite-time control of positive impulsive switched systems. International Journal of Control, Automation and Systems18(2): 1751–1757.
21.
LiuXSuXShiP, et al. (2019) Fault detection filtering for nonlinear switched systems via event-triggered communication approach. Automatica101: 365–376.
22.
LuJLiuC (2007) Realization of fractional-order Liu chaotic system by circuit. Chinese Physics B16(6): 1586–590.
23.
MelicioRMendesVCatalaoJ (2010) Fractional-order control and simulation of wind energy systems with PMSG/full-power converter topology. Energy Conversion and Management51(6): 1250–1258.
24.
NingZWangTSongX, et al. (2019a) Fault detection of nonlinear stochastic systems via a dynamic event-triggered strategy. Signal Processing167: 107283.
25.
NingZYuJWangT (2019b) Event-triggered fault detection filter design for uncertain stochastic network system with package dropouts. Institution of Mechanical Engineers Part I: Journal of Systems and Control Engineering233(10): 1351–1360.
26.
NingZYuJWangT (2019c) fault detection filter design for discrete-time stochastic systems with limited communication. Transactions of the Institute of Measurement and Control41(13): 3808–3817.
27.
PetrasI (2011) Fractional-order memristor-based Chua’s circuit. IEEE Transactions on Circuits and Systems II Express Briefs57(12): 975–979.
28.
QiYCaoZLiX (2019) Decentralized event-triggered control for switched systems with network communication delay. Journal of the Franklin Institute356(3): 1424–1445.
29.
QiYLiuYBaoW, et al. (2018) Event-triggered and guaranteed cost finite-time control for uncertain switched linear systems. Optimal Control Applications & Methods39(4): 1337–1353.
30.
RenGYuYXuC, et al. (2019) Consensus of fractional multi-agent systems by distributed event-triggered strategy. Nonlinear Dynamics95(1): 541–555.
31.
ThuanMBinhTHuongD (2020) Finite-time guaranteed cost control of caputo fractional-order neural networks. Asian Journal of Control22(2): 696–705.
32.
WangFYangY (2017) Leader-following consensus of nonlinear fractional-order multi-agent systems via event-triggered control. International Journal of Systems Science48(3): 571–577.
33.
WuCSiGZhangY, et al. (2015) The fractional-order state-space averaging modeling of the BuckCBoost DC/DC converter in discontinuous conduction mode and the performance analysis. Nonlinear Dynamics79(1): 689–703.
34.
XuHTeoK-LLiuX (2008) Robust stability analysis of guaranteed cost control for impulsive switched systems. IEEE Transactions on Systems, Man and Cybernetics Part B38(5): 1419–1422.
35.
YangYChenG (2015) Finite-time stability of fractional order impulsive switched systems. International Journal of Robust and Nonlinear Control25(13): 2207–2222.
36.
YeYSuH (2018) Leader-following consensus of general linear fractional-order multiagent systems with input delay via event-triggered control. International Journal of Robust and Nonlinear Control28(18): 5717–5729.
37.
ZhangJZhaoXChenY (2016) Finite-time stability and stabilization of fractional order positive switched systems. Circuits, Systems, and Signal Processing35(7): 2450–2470.
38.
ZhangJZhaoXZhuF, et al. (2020) Reduced-order observer design for switched descriptor systems with unknown inputs. IEEE Transactions on Automatic Control65(1): 287–294.
39.
ZhangJZhuFKarimiHR, et al. (2019) Observer-based sliding mode control for T-S fuzzy descriptor systems with time delay. IEEE Transactions on Fuzzy Systems27(10): 2009–2023.
40.
ZhaoXYinYZhengX (2016) State-dependent switching control of switched positive fractional-order systems. ISA Transactions62(S1): 103–108.
