This article proposes a new sliding mode control strategy for stabilizing controller design for fractional-order Markovian jump systems. The suggested approach is based on the diffusive representation of fractional-order Markovian jump systems which transforms the fractional-order system into an integer-order one. Using a new Lyapunov–Krasovskii functional, the problem of sliding mode control of uncertain fractional-order Markovian jump systems with exogenous noise is investigated. We propose a sliding surface and prove its reachability. Moreover, the linear matrix inequality conditions for stochastic stability of the resultant sliding motion with a given disturbance attenuation level are derived. Eventually, the theoretical results are verified through a simulation example.
LinZLiuJWuQ, et al. Mixed H2/H∞ pitch control of wind turbine with a Markovian jump model. Int J Control2018; 91(1): 156–169.
2.
LiYKarimiHRZhaoD, et al. H∞ fault detection filter design for discrete-time nonlinear Markovian jump systems with missing measurements. Europ J Control2018; 44: 27–39.
3.
YangHLiHSunF, et al. Robust control for Markovian jump delta operator systems with actuator saturation. Europ J Control2014; 20(4): 207–215.
4.
LinJFeiSShenJ, et al. Exponential estimates and H∞ control for singular Markovian jump systems with interval time-varying delay. Proc IMechE, Part I: J Systems and Control Engineering2010; 224(4): 437–456.
5.
AliMSYogambigaiJSaravananS, et al. Stochastic stability of neutral-type Markovian-jumping BAM neural networks with time varying delays. J Comput Appl Math2019; 349: 142–156.
6.
MaLWangZHanQL, et al. Dissipative control for nonlinear Markovian jump systems with actuator failures and mixed time-delays. Automatica2018; 98: 358–362.
7.
WangBChengJZouF.Stochastic finite-time H∞ filtering for nonlinear Markovian jump systems with partly known transition probabilities. Proc IMechE, Part I: J Systems and Control Engineering2019; 233(1): 31–43.
8.
KhandaniKMajdVJTahmasebiM.Integral sliding mode control for robust stabilisation of uncertain stochastic time-delay systems driven by fractional Brownian motion. Int J Syst Sci2017; 48(4): 828–837.
9.
EsfahaniZRoohiMGheisarnejadM, et al. Optimal non-integer sliding mode control for frequency regulation in stand-alone modern power grids. Appl Sci2019; 9(16): 3411.
10.
KhandaniKMajdVJTahmasebiM.Robust stabilization of uncertain time-delay systems with fractional stochastic noise using the novel fractional stochastic sliding approach and its application to stream water quality regulation. IEEE T Automat Control2016; 62(4): 1742–1751.
11.
YaghootiBSiahi ShadbadASafaviK, et al. Adaptive synchronization of uncertain fractional-order chaotic systems using sliding mode control techniques. Proc IMechE, Part I: J Systems and Control Engineering2020; 234(1): 3–9.
12.
JiangBKarimiHRKaoY, et al. Reduced-order adaptive sliding mode control for nonlinear switching semi-Markovian jump delayed systems. Inform Sci2019; 477: 334–348.
13.
ZhaoWMaYChenA, et al. Robust sliding mode control for Markovian jump singular systems with randomly changing structure. Appl Math Comput2019; 349: 81–96.
14.
ShenMZhangHParkJH.Observer-based quantized sliding mode H∞ control of Markov jump systems. Nonlin Dynam2018; 92(2): 415–427.
15.
XuCTongDChenQ, et al. Exponential stability of Markovian jumping systems via adaptive sliding mode control. IEEE T Syst Man Cyb Syst. Epub ahead of print 8January2019. DOI: 10.1109/TSMC.2018.2884565.
16.
ZhangPHuJZhangH, et al. H∞ sliding mode control for Markovian jump systems with randomly occurring uncertainties and repeated scalar nonlinearities via delay-fractioning method. ISA Trans2020; 101: 10–22.
17.
LiFDuCYangC, et al. Finite-time asynchronous sliding mode control for Markovian jump systems. Automatica2019; 109: 108503.
18.
NieRHeSLuanX, et al. Fixed-time sliding mode controller design for a class of nonlinear Markovian jumping systems. J Frankl Inst2020; 357: 10227–10243.
19.
MaRShaoXLiuJ, et al. Event-triggered sliding mode control of Markovian jump systems against input saturation. Syst Control Lett2019; 134: 104525.
20.
ParvizianMKhandaniKMajdVJ.A non-fragile observer-based adaptive sliding mode control for fractional-order Markovian jump systems with time delay and input nonlinearity. Trans Inst Meas Control2020; 42(8): 1448–1460.
21.
ParvizianMKhandaniKMajdVJ.An H∞ non-fragile observer-based adaptive sliding mode controller design for uncertain fractional-order nonlinear systems with time delay and input nonlinearity. Asian J Control2020; 42: 1448–1460.
22.
KheirizadIJalaliAAKhandaniK.Stabilization of fractional-order unstable delay systems by fractional-order controllers. Proc IMechE, Part I: J Systems and Control Engineering2012; 226(9): 1166–1173.
23.
IzadbakhshAKheirkhahanP.Adaptive fractional-order control of electrical flexible-joint robots: theory and experiment. Proc IMechE, Part I: J Systems and Control Engineering2019; 233(9): 1136–1145.
24.
HafeziAKhandaniKMajdVJ.Non-fragile exponential polynomial observer design for a class of nonlinear fractional-order systems with application in chaotic communication and synchronisation. Int J Syst Sci2020; 51(8): 1353–1372.
25.
KheirizadIJalaliAAKhandaniK.Stabilization of all-pole unstable delay systems by fractional-order [PI] and [PD] controllers. Trans Inst Meas Control2013; 35(3): 257–266.
26.
SunHZhangYBaleanuD, et al. A new collection of real world applications of fractional calculus in science and engineering. Commun Nonlin Sci Numer Simul2018; 64: 213–231.
27.
MontsenyG.Diffusive representation of pseudo-differential time-operators. ESIAM1998; 5: 159–175.
28.
BettayebMDjennouneS.Design of sliding mode controllers for nonlinear fractional-order systems via diffusive representation. Nonlin Dynam2016; 84(2): 593–605.
29.
PodlubnyI.Fractional differential equations. New York: Academic Press, 1999.
30.
ChenBNiuYZouY.Adaptive sliding mode control for stochastic Markovian jumping systems with actuator degradation. Automatica2013; 49(6): 1748–1754.
31.
SaravanakumarRAliMSKarimiHR.Robust H∞ control of uncertain stochastic Markovian jump systems with mixed time-varying delays. Int J Syst Sci2017; 48(4): 862–872.
32.
BoydSEl GhaouiLFeronE, et al. Linear matrix inequalities in system and control theory, Vol. 15. Philadelphia, PA: Society for Industrial and Applied Mathematics1994.
33.
KhasminskiiR.Stochastic stability of differential equations. New York: Springer, 2012.
