Xu, Gen Qi Resolvent family for the evolution process with memory. (English) Zbl 1527.34106 Math. Nachr. 296, No. 6, 2626-2656 (2023). Reviewer: Sotiris K. Ntouyas (Ioannina) MSC: 34K05 34K30 34K06 47A10 PDFBibTeX XMLCite \textit{G. Q. Xu}, Math. Nachr. 296, No. 6, 2626--2656 (2023; Zbl 1527.34106) Full Text: DOI
Zhang, Hai-E.; Xu, Gen-Qi; Chen, Hao; Li, Min Stability of a variable coefficient star-shaped network with distributed delay. (English) Zbl 1521.93160 J. Syst. Sci. Complex. 35, No. 6, 2077-2106 (2022). MSC: 93D23 93B70 93C20 93C43 PDFBibTeX XMLCite \textit{H.-E. Zhang} et al., J. Syst. Sci. Complex. 35, No. 6, 2077--2106 (2022; Zbl 1521.93160) Full Text: DOI
Xu, Genqi Some problems of linear differential equations on abstract spaces and unbounded perturbations of linear operator semigroup. (English) Zbl 1496.93063 Front. Math. China 17, No. 1, 47-77 (2022); translation from Adv. Math., Beijing 48, No. 6, 641–666 (2019). MSC: 93C25 47D06 35L20 93B52 PDFBibTeX XMLCite \textit{G. Xu}, Front. Math. China 17, No. 1, 47--77 (2022; Zbl 1496.93063); translation from Adv. Math., Beijing 48, No. 6, 641--666 (2019) Full Text: DOI
Rahmtati, Alireza Jalili; Xu, Genqi; Effati, Sohrab Stability analysis of the Euler-Bernoulli beam with multi-delay controller. (English) Zbl 1500.93092 Control Theory Technol. 20, No. 3, 338-348 (2022). MSC: 93D05 93C20 93B52 74K10 PDFBibTeX XMLCite \textit{A. J. Rahmtati} et al., Control Theory Technol. 20, No. 3, 338--348 (2022; Zbl 1500.93092) Full Text: DOI
Wang, Xiaorui; Xu, Genqi; Chen, Hao Uniform stabilization of 1-D Schrödinger equation with internal difference-type control. (English) Zbl 1480.35133 Discrete Contin. Dyn. Syst., Ser. B 26, No. 12, 6359-6376 (2021). MSC: 35J10 93C20 93D15 PDFBibTeX XMLCite \textit{X. Wang} et al., Discrete Contin. Dyn. Syst., Ser. B 26, No. 12, 6359--6376 (2021; Zbl 1480.35133) Full Text: DOI
Xu, Genqi; Li, Min Stability of wave networks on elastic and viscoelastic media. (English) Zbl 1476.35055 Acta Appl. Math. 175, Paper No. 11, 40 p. (2021). MSC: 35B40 35L53 35Q74 PDFBibTeX XMLCite \textit{G. Xu} and \textit{M. Li}, Acta Appl. Math. 175, Paper No. 11, 40 p. (2021; Zbl 1476.35055) Full Text: DOI
Zhang, Li; Xu, Gen Qi; Chen, Hao Uniform stabilization of 1-d wave equation with anti-damping and delayed control. (English) Zbl 1454.93242 J. Franklin Inst. 357, No. 17, 12473-12494 (2020). MSC: 93D23 93C20 35L05 PDFBibTeX XMLCite \textit{L. Zhang} et al., J. Franklin Inst. 357, No. 17, 12473--12494 (2020; Zbl 1454.93242) Full Text: DOI
Xu, Gen Qi; Zhang, Li Uniform stabilization of 1-D coupled wave equations with anti-dampings and joint delayed control. (English) Zbl 1453.93204 SIAM J. Control Optim. 58, No. 6, 3161-3184 (2020). MSC: 93D23 93C20 35L05 93B17 93B52 PDFBibTeX XMLCite \textit{G. Q. Xu} and \textit{L. Zhang}, SIAM J. Control Optim. 58, No. 6, 3161--3184 (2020; Zbl 1453.93204) Full Text: DOI
Wang, Xiaorui; Xu, Genqi Uniform stabilization of a wave equation with partial Dirichlet delayed control. (English) Zbl 1443.35092 Evol. Equ. Control Theory 9, No. 2, 509-533 (2020). Reviewer: Kaïs Ammari (Monastir) MSC: 35L20 35L05 93C20 93D15 35G15 PDFBibTeX XMLCite \textit{X. Wang} and \textit{G. Xu}, Evol. Equ. Control Theory 9, No. 2, 509--533 (2020; Zbl 1443.35092) Full Text: DOI
Liu, Dongyi; Han, Rumeng; Xu, Genqi Controller design for distributed parameter systems with time delays in the boundary feedbacks via the backstepping method. (English) Zbl 1443.93113 Int. J. Control 93, No. 5, 1220-1230 (2020). MSC: 93D23 93B52 93C20 93C43 PDFBibTeX XMLCite \textit{D. Liu} et al., Int. J. Control 93, No. 5, 1220--1230 (2020; Zbl 1443.93113) Full Text: DOI
Feng, Xiaoxuan; Xu, Genqi; Chen, Yunlan Rapid stabilisation of an Euler-Bernoulli beam with the internal delay control. (English) Zbl 1415.93216 Int. J. Control 92, No. 1, 42-55 (2019). MSC: 93D20 74K10 93C25 70Q05 93B52 93B17 PDFBibTeX XMLCite \textit{X. Feng} et al., Int. J. Control 92, No. 1, 42--55 (2019; Zbl 1415.93216) Full Text: DOI
Shang, YingFeng; Xu, Genqi Dynamic control of an Euler-Bernoulli equation with time-delay and disturbance in the boundary control. (English) Zbl 1415.93117 Int. J. Control 92, No. 1, 27-41 (2019). MSC: 93B52 93C20 93D05 93D15 PDFBibTeX XMLCite \textit{Y. Shang} and \textit{G. Xu}, Int. J. Control 92, No. 1, 27--41 (2019; Zbl 1415.93117) Full Text: DOI
Xie, Ya-Ru; Han, Zhong-Jie; Xu, Gen-Qi Stabilization of serially connected hybrid PDE-ODE system with unknown external disturbances. (English) Zbl 1408.93106 Appl. Anal. 98, No. 4, 718-734 (2019). MSC: 93D15 93C15 93C20 93B12 93B52 47N70 93B28 PDFBibTeX XMLCite \textit{Y.-R. Xie} et al., Appl. Anal. 98, No. 4, 718--734 (2019; Zbl 1408.93106) Full Text: DOI
Cui, Haoyue; Liu, Dongyi; Xu, Genqi Asymptotic behavior of a Schrödinger equation under a constrained boundary feedback. (English) Zbl 1406.81024 Math. Control Relat. Fields 8, No. 2, 383-395 (2018). MSC: 81Q05 93D15 93D20 35B40 65N35 47H05 81T80 81Q93 PDFBibTeX XMLCite \textit{H. Cui} et al., Math. Control Relat. Fields 8, No. 2, 383--395 (2018; Zbl 1406.81024) Full Text: DOI
Xu, Gen Qi Necessary condition of linear distributed parameter systems with exact controllability. (English) Zbl 1402.93058 Syst. Control Lett. 118, 109-115 (2018). MSC: 93B05 93C05 93C25 PDFBibTeX XMLCite \textit{G. Q. Xu}, Syst. Control Lett. 118, 109--115 (2018; Zbl 1402.93058) Full Text: DOI
Geng, Huan; Han, Zhong-Jie; Wang, Jing; Xu, Gen-Qi Stabilization of a nonlinear rotating disk-beam system with localized thermal effect. (English) Zbl 1398.93285 Nonlinear Dyn. 93, No. 2, 785-799 (2018). MSC: 93D15 93D20 35Q93 93C20 74K10 74F05 PDFBibTeX XMLCite \textit{H. Geng} et al., Nonlinear Dyn. 93, No. 2, 785--799 (2018; Zbl 1398.93285) Full Text: DOI
Li, Yanfang; Xu, Genqi; Han, Zhongjie Feedback stabilisation of an Euler-Bernoulli beam with the boundary time-delay disturbance. (English) Zbl 1397.93169 Int. J. Control 91, No. 8, 1835-1847 (2018). MSC: 93D15 93D30 93C30 74K10 PDFBibTeX XMLCite \textit{Y. Li} et al., Int. J. Control 91, No. 8, 1835--1847 (2018; Zbl 1397.93169) Full Text: DOI
Xie, Y. R.; Xu, G. Q. Stabilization of a wave equation with a tip mass based on disturbance observer of time-varying gain. (English) Zbl 1372.35175 J. Dyn. Control Syst. 23, No. 4, 667-677 (2017). MSC: 35L05 35L20 34H15 PDFBibTeX XMLCite \textit{Y. R. Xie} and \textit{G. Q. Xu}, J. Dyn. Control Syst. 23, No. 4, 667--677 (2017; Zbl 1372.35175) Full Text: DOI
Xu, Genqi; Feng, Xiaoyu; Kwok, Ki Lung The exponential stability region of Timoshenko beam with interior delays and boundary damping. (English) Zbl 1367.93576 Int. J. Control 90, No. 8, 1529-1542 (2017). MSC: 93D20 74K10 93C20 47D03 PDFBibTeX XMLCite \textit{G. Xu} et al., Int. J. Control 90, No. 8, 1529--1542 (2017; Zbl 1367.93576) Full Text: DOI
Liu, Xiu-Fang; Xu, Gen-Qi Exponential stabilization of Timoshenko beam with input and output delays. (English) Zbl 1347.93220 Math. Control Relat. Fields 6, No. 2, 271-292 (2016). MSC: 93D21 93C20 93B52 93D15 74K10 PDFBibTeX XMLCite \textit{X.-F. Liu} and \textit{G.-Q. Xu}, Math. Control Relat. Fields 6, No. 2, 271--292 (2016; Zbl 1347.93220) Full Text: DOI
Guo, Yanni; Xu, Genqi; Guo, Yansha Stabilization of the wave equation with interior input delay and mixed Neumann-Dirichlet boundary. (English) Zbl 1350.35104 Discrete Contin. Dyn. Syst., Ser. B 21, No. 8, 2491-2507 (2016). MSC: 35L20 35B35 93D15 93C20 PDFBibTeX XMLCite \textit{Y. Guo} et al., Discrete Contin. Dyn. Syst., Ser. B 21, No. 8, 2491--2507 (2016; Zbl 1350.35104) Full Text: DOI
Cui, Hao-Yue; Han, Zhong-Jie; Xu, Gen-Qi Stabilization for Schrödinger equation with a time delay in the boundary input. (English) Zbl 1342.35082 Appl. Anal. 95, No. 5, 963-977 (2016). Reviewer: Christian Seifert (Hamburg) MSC: 35J10 93C20 93D15 93D20 PDFBibTeX XMLCite \textit{H.-Y. Cui} et al., Appl. Anal. 95, No. 5, 963--977 (2016; Zbl 1342.35082) Full Text: DOI
Liu, Xiu Fang; Xu, Gen Qi Output-based stabilization of Timoshenko beam with the boundary control and input distributed delay. (English) Zbl 1337.93072 J. Dyn. Control Syst. 22, No. 2, 347-367 (2016). MSC: 93D15 93C20 74K10 93D20 70Q05 PDFBibTeX XMLCite \textit{X. F. Liu} and \textit{G. Q. Xu}, J. Dyn. Control Syst. 22, No. 2, 347--367 (2016; Zbl 1337.93072) Full Text: DOI
Liu, Dongyi; Zhang, Liping; Xu, Genqi Stabilisation of Timoshenko beam system with a tip payload under the unknown boundary external disturbances. (English) Zbl 1338.93303 Int. J. Control 88, No. 9, 1830-1840 (2015). MSC: 93D15 93C73 74K10 70Q05 93D20 47H05 PDFBibTeX XMLCite \textit{D. Liu} et al., Int. J. Control 88, No. 9, 1830--1840 (2015; Zbl 1338.93303) Full Text: DOI
Shang, Ying Feng; Xu, Gen Qi Dynamic feedback control and exponential stabilization of a compound system. (English) Zbl 1297.93131 J. Math. Anal. Appl. 422, No. 2, 858-879 (2015). MSC: 93D15 93B52 70Q05 74K10 35Q93 34H05 PDFBibTeX XMLCite \textit{Y. F. Shang} and \textit{G. Q. Xu}, J. Math. Anal. Appl. 422, No. 2, 858--879 (2015; Zbl 1297.93131) Full Text: DOI
Chen, Yun Lan; Xu, Gen Qi Exponential stability of uniform Euler-Bernoulli beams with non-collocated boundary controllers. (English) Zbl 1305.93175 J. Math. Anal. Appl. 409, No. 2, 851-867 (2014). MSC: 93D20 93B60 74K10 PDFBibTeX XMLCite \textit{Y. L. Chen} and \textit{G. Q. Xu}, J. Math. Anal. Appl. 409, No. 2, 851--867 (2014; Zbl 1305.93175) Full Text: DOI
Xu, Gen Qi State reconstruction of a distributed parameter system with exact observability. (English) Zbl 1305.93042 J. Math. Anal. Appl. 409, No. 1, 168-179 (2014). MSC: 93B07 34H05 93B30 93B28 PDFBibTeX XMLCite \textit{G. Q. Xu}, J. Math. Anal. Appl. 409, No. 1, 168--179 (2014; Zbl 1305.93042) Full Text: DOI
Liu, Xiu Fang; Xu, Gen Qi Exponential stabilization for Timoshenko beam with distributed delay in the boundary control. (English) Zbl 1421.93120 Abstr. Appl. Anal. 2013, Article ID 726794, 15 p. (2013). MSC: 93D20 74K10 70Q05 PDFBibTeX XMLCite \textit{X. F. Liu} and \textit{G. Q. Xu}, Abstr. Appl. Anal. 2013, Article ID 726794, 15 p. (2013; Zbl 1421.93120) Full Text: DOI
Zhang, Kuiting; Xu, Genqi A pinned network of Euler-Bernoulli beams under feedback controls. (English) Zbl 1282.93131 J. Syst. Sci. Complex. 26, No. 3, 313-334 (2013). MSC: 93B52 93C25 93D20 PDFBibTeX XMLCite \textit{K. Zhang} and \textit{G. Xu}, J. Syst. Sci. Complex. 26, No. 3, 313--334 (2013; Zbl 1282.93131) Full Text: DOI
Xu, Genqi; Wang, Hongxia Stabilisation of Timoshenko beam system with delay in the boundary control. (English) Zbl 1278.93221 Int. J. Control 86, No. 6, 1165-1178 (2013). MSC: 93D20 70Q05 93B07 93B52 93C20 PDFBibTeX XMLCite \textit{G. Xu} and \textit{H. Wang}, Int. J. Control 86, No. 6, 1165--1178 (2013; Zbl 1278.93221) Full Text: DOI
Shang, Ying Feng; Xu, Gen Qi; Chen, Yun Lan Stability analysis of Euler-Bernoulli beam with input delay in the boundary control. (English) Zbl 1282.93199 Asian J. Control 14, No. 1, 186-196 (2012). MSC: 93D05 70Q05 74K10 93C20 93B52 PDFBibTeX XMLCite \textit{Y. F. Shang} et al., Asian J. Control 14, No. 1, 186--196 (2012; Zbl 1282.93199) Full Text: DOI
Han, Zhong-Jie; Xu, Gen-Qi Stabilization and SDG condition of serially connected vibrating strings system with discontinuous displacement. (English) Zbl 1282.93207 Asian J. Control 14, No. 1, 95-108 (2012). MSC: 93D15 93B52 93B60 93C20 93D20 PDFBibTeX XMLCite \textit{Z.-J. Han} and \textit{G.-Q. Xu}, Asian J. Control 14, No. 1, 95--108 (2012; Zbl 1282.93207) Full Text: DOI
Shang, Ying Feng; Xu, Gen Qi Stabilization of an Euler-Bernoulli beam with input delay in the boundary control. (English) Zbl 1252.93100 Syst. Control Lett. 61, No. 11, 1069-1078 (2012). MSC: 93D15 74K10 93C20 93D20 PDFBibTeX XMLCite \textit{Y. F. Shang} and \textit{G. Q. Xu}, Syst. Control Lett. 61, No. 11, 1069--1078 (2012; Zbl 1252.93100) Full Text: DOI
Xu, Gen Qi The structural property of a class of vector-valued hyperbolic equations and applications. (English) Zbl 1233.35138 J. Math. Anal. Appl. 388, No. 1, 566-592 (2012). MSC: 35L57 74K10 35Q74 35P10 PDFBibTeX XMLCite \textit{G. Q. Xu}, J. Math. Anal. Appl. 388, No. 1, 566--592 (2012; Zbl 1233.35138) Full Text: DOI
Chen, Yunlan; Han, Zhongjie; Xu, Genqi; Liu, Dongyi Exponential stability of string system with variable coefficients under non-collocated feedback controls. (English) Zbl 1248.93142 Asian J. Control 13, No. 1, 148-163 (2011). MSC: 93D20 93D15 93B52 PDFBibTeX XMLCite \textit{Y. Chen} et al., Asian J. Control 13, No. 1, 148--163 (2011; Zbl 1248.93142) Full Text: DOI
Guo, Yanni; Xu, Genqi Asymptotic stability and Riesz basis property for tree-shaped network of strings. (English) Zbl 1226.93118 J. Syst. Sci. Complex. 24, No. 2, 225-252 (2011). MSC: 93D20 93B52 93B28 PDFBibTeX XMLCite \textit{Y. Guo} and \textit{G. Xu}, J. Syst. Sci. Complex. 24, No. 2, 225--252 (2011; Zbl 1226.93118) Full Text: DOI
Han, Zhong-Jie; Xu, Gen-Qi Dynamical behavior of a hybrid system of nonhomogeneous Timoshenko beam with partial non-collocated inputs. (English) Zbl 1211.93054 J. Dyn. Control Syst. 17, No. 1, 77-121 (2011). MSC: 93B52 93D15 34B05 93C20 93C30 70Q05 PDFBibTeX XMLCite \textit{Z.-J. Han} and \textit{G.-Q. Xu}, J. Dyn. Control Syst. 17, No. 1, 77--121 (2011; Zbl 1211.93054) Full Text: DOI
Xu, Gen Qi; Shang, Ying Feng Characteristic of left invertible semigroups and admissibility of observation operators. (English) Zbl 1170.47028 Syst. Control Lett. 58, No. 8, 561-566 (2009). Reviewer: Birgit Jacob (Paderborn) MSC: 47D06 93B07 93C25 PDFBibTeX XMLCite \textit{G. Q. Xu} and \textit{Y. F. Shang}, Syst. Control Lett. 58, No. 8, 561--566 (2009; Zbl 1170.47028) Full Text: DOI
Xu, Gen Qi; Liu, Chao; Yung, Siu Pang Necessary conditions for the exact observability of systems on Hilbert spaces. (English) Zbl 1130.93019 Syst. Control Lett. 57, No. 3, 222-227 (2008). MSC: 93B05 93C05 93C15 PDFBibTeX XMLCite \textit{G. Q. Xu} et al., Syst. Control Lett. 57, No. 3, 222--227 (2008; Zbl 1130.93019) Full Text: DOI
Guo, Bao-Zhu; Xu, Gen-Qi Expansion of solution in terms of generalized eigenfunctions for a hyperbolic system with static boundary condition. (English) Zbl 1153.35368 J. Funct. Anal. 231, No. 2, 245-268 (2006). MSC: 35P10 47A10 35L50 93B28 93C20 PDFBibTeX XMLCite \textit{B.-Z. Guo} and \textit{G.-Q. Xu}, J. Funct. Anal. 231, No. 2, 245--268 (2006; Zbl 1153.35368) Full Text: DOI
Vu, Quoc-Phong; Wang, Jun-Min; Xu, Genqi; Yung, Siu-Pang Spectral analysis and system of fundamental solutions for Timoshenko beams. (English) Zbl 1070.74020 Appl. Math. Lett. 18, No. 2, 127-134 (2005). MSC: 74H45 74K10 74H10 PDFBibTeX XMLCite \textit{Q.-P. Vu} et al., Appl. Math. Lett. 18, No. 2, 127--134 (2005; Zbl 1070.74020) Full Text: DOI
Guo, Bao-Zhu; Xu, Gen-Qi Riesz bases and exact controllability of \(c_{0}-groups\) with one-dimensional input operators. (English) Zbl 1157.93331 Syst. Control Lett. 52, No. 3-4, 221-232 (2004). MSC: 93B07 34G10 47D06 47N70 93C20 93C25 PDFBibTeX XMLCite \textit{B.-Z. Guo} and \textit{G.-Q. Xu}, Syst. Control Lett. 52, No. 3--4, 221--232 (2004; Zbl 1157.93331) Full Text: DOI
Xu, G. Q.; Yung, S. P. Exponential decay rate for a Timoshenko beam with boundary damping. (English) Zbl 1068.35172 J. Optimization Theory Appl. 123, No. 3, 669-693 (2004). Reviewer: Gheorghe Aniculăesei (Iaşi) MSC: 35Q72 74H55 74K10 35B40 PDFBibTeX XMLCite \textit{G. Q. Xu} and \textit{S. P. Yung}, J. Optim. Theory Appl. 123, No. 3, 669--693 (2004; Zbl 1068.35172) Full Text: DOI