Similar articles

Abstract: In this paper, observer-based control for fractional-order singular systems with order α (0<α<1) and input delay is studied. On the basis of the Smith predictor and approximation error, the system with input delay is approximately equivalent to the system without input delay. Furthermore, based on the linear matrix inequality (LMI) technique, the necessary and sufficient condition of observer-based control is proposed. Since the condition is a nonstrict LMI, including the equality constraint, it will lead to some trouble when solving problems using toolbox. Thus, the strict LMI-based condition is improved in the paper. Finally, a numerical example and a direct current motor example are given to illustrate the effectiveness of the strict LMI-based condition.

输入时滞分数阶(0<α<1)奇异系统的观测器控制

[1]Aghayan ZS, Alfi A, Tenreiro Machado JA, 2021. Stability analysis of uncertain fractional-order neutral-type delay systems with actuator saturation. Front Inform Technol Electron Eng, 22(10):1402-1412.

[2]Du FF, Lu JG, 2021. Explicit solutions and asymptotic behaviors of Caputo discrete fractional-order equations with variable coefficients. Chaos Sol Fract, 153:111490.

[3]Geng WT, Lin C, Chen B, 2020. Observer-based stabilizing control for fractional-order systems with input delay. ISA Trans, 100:103-108.

[4]Guerrero JC, Chávez-Fuentes JR, Casavilca JE, et al., 2021. Stability analysis of discrete-time Markov jump linear singular systems with partially known transition probabilities. Syst Contr Lett, 158:105057.

[5]Hua CC, Ning JH, Guan XP, 2021. Controller design for fractional-order interconnected systems with unmodeled dynamics. Nonl Dynam, 103(2):1599-1610.

[6]Ibrir S, Bettayeb M, 2015. New sufficient conditions for observer-based control of fractional-order uncertain systems. Automatica, 59:216-223.

[7]Ji YD, Qiu JQ, 2015. Stabilization of fractional-order singular uncertain systems. ISA Trans, 56:53-64.

[8]Jiang LQ, Wang ST, Xie YL, et al., 2022. Fractional robust finite time control of four-wheel-steering mobile robots subject to serious time-varying perturbations. Mech Mach Theory, 169:104634.

[9]Lan YH, Zhou Y, 2013. Non-fragile observer-based robust control for a class of fractional-order nonlinear systems. Syst Contr Lett, 62(12):1143-1150.

[10]Lan YH, Huang HX, Zhou Y, 2012. Observer-based robust control of α (1≤α<2) fractional-order uncertain systems: a linear matrix inequality approach. IET Contr Theory Appl, 6(2):229-234.

[11]Léchappé V, Rouquet S, González A, et al., 2016. Delay estimation and predictive control of uncertain systems with input delay: application to a DC motor. IEEE Trans Ind Electron, 63(9):5849-5857.

[12]Lee DH, 2020. Balanced parallel instantaneous position control of PMDC motors with low-cost position sensors. J Power Electron, 20(3):834-843.

[13]Li BX, Zhang XF, 2016. Observer-based robust control of fractional-order linear uncertain control systems. IET Contr Theory Appl, 10(14):1724-1731.

[14]Li C, Wang JC, Lu JG, et al., 2014. Observer-based stabilisation of a class of fractional order non-linear systems for 0<α<2 case. IET Contr Theory Appl, 8(13):1238-1246.

[15]Li H, Yang GH, 2019. Dynamic output feedback H_∞control for fractional-order linear uncertain systems with actuator faults. J Frankl Inst, 356(8):4442-4466.

[16]Li RC, Zhang XF, 2020. Adaptive sliding mode observer design for a class of T-S fuzzy descriptor fractional order systems. IEEE Trans Fuzzy Syst, 28(9):1951-1960.

[17]Li YC, Ma SP, 2021. Finite and infinite horizon indefinite linear quadratic optimal control for discrete-time singular Markov jump systems. J Frankl Inst, 358(17):8993-9022.

[18]Lin C, Chen B, Shi P, et al., 2018. Necessary and sufficient conditions of observer-based stabilization for a class of fractional-order descriptor systems. Syst Contr Lett, 112:31-35.

[19]Lu JG, Chen GR, 2009. Robust stability and stabilization of fractional-order interval systems: an LMI approach. IEEE Trans Autom Contr, 54(6):1294-1299.

[20]Lu JG, Chen YQ, 2010. Robust stability and stabilization of fractional-order interval systems with the fractional order α: the 0<α<1 case. IEEE Trans Autom Contr, 55(1):152-158.

[21]Marir S, Chadli M, 2019. Robust admissibility and stabilization of uncertain singular fractional-order linear time-invariant systems. IEEE/CAA J Autom Sin, 6(3):685-692.

[22]Marir S, Chadli M, Bouagada D, 2017. New admissibility conditions for singular linear continuous-time fractional-order systems. J Frankl Inst, 354(2):752-766.

[23]Marir S, Chadli M, Basin MV, 2022a. Bounded real lemma for singular linear continuous-time fractional-order systems. Automatica, 135:109962.

[24]Marir S, Chadli M, Basin MV, 2022b. H_∞ static output feedback controller design for singular fractional-order systems. Proc European Control Conf, p.1-6.

[25]Matignon D, 1998. Stability properties for generalized fractional differential systems. ESAIM Proc, 5:145-158.

[26]N’Doye I, Darouach M, Zasadzinski M, et al., 2013. Robust stabilization of uncertain descriptor fractional-order systems. Automatica, 49(6):1907-1913.

[27]Nguyen CM, Tan CP, Trinh H, 2021. State and delay reconstruction for nonlinear systems with input delays. Appl Math Comput, 390:125609.

[28]Pu YF, Wang J, 2020. Fractional-order global optimal backpropagation machine trained by an improved fractional-order steepest descent method. Front Inform Technol Electron Eng, 21(6):809-833.

[29]Sabatier J, Moze M, Farges C, 2010. LMI stability conditions for fractional order systems. Comput Math Appl, 59(5):1594-1609.

[30]Saffarian M, Mohebbi A, 2021. Numerical solution of two and three dimensional time fractional damped nonlinear Klein-Gordon equation using ADI spectral element method. Appl Math Comput, 405:126182.

[31]Si-Ammour A, Djennoune S, Bettayeb M, 2009. A sliding mode control for linear fractional systems with input and state delays. Commun Nonl Sci Numer Simul, 14(5):2310-2318.

[32]Stamova I, 2014. Global stability of impulsive fractional differential equations. Appl Math Comput, 237:605-612.

[33]Udhayakumar K, Rakkiyappan R, Cao JD, et al., 2020. Mittag-Leffler stability analysis of multiple equilibrium points in impulsive fractional-order quaternion-valued neural networks. Front Inform Technol Electron Eng, 21(2):234-246.

[34]Wei YH, Wang JC, Liu TY, et al., 2019. Sufficient and necessary conditions for stabilizing singular fractional order systems with partially measurable state. J Frankl Inst, 356(4):1975-1990.

[35]Wu Q, Song QK, Hu BX, et al., 2020. Robust stability of uncertain fractional order singular systems with neutral and time-varying delays. Neurocomputing, 401:145-152.

[36]Xu SY, Lam J, 2006. Robust Control and Filtering of Singular Systems. Springer, Berlin, Germany.

[37]Xu SY, van Dooren P, Stefan R, et al., 2002. Robust stability and stabilization for singular systems with state delay and parameter uncertainty. IEEE Trans Autom Contr, 47(7):1122-1128.

[38]Zhang L, Niu B, Zhao N, et al., 2021. Reachable set estimation of singular semi-Markov jump systems. J Frankl Inst, in press.

[39]Zhang XF, Chen YQ, 2018. Admissibility and robust stabilization of continuous linear singular fractional order systems with the fractional order α: the 0<α<1 case. ISA Trans, 82:42-50.