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A nonlinear wave equation with jumping nonlinearity
A gradient flow approach for computing jump linear quadratic optimal feedback gains
1.  Department of Computational and Applied Mathematics, University of The Witwatersrand, Johannesburg, South Africa, South Africa, South Africa 
[1] 
Jian Chen, Tao Zhang, Ziye Zhang, Chong Lin, Bing Chen. Stability and output feedback control for singular Markovian jump delayed systems. Mathematical Control & Related Fields, 2018, 8 (2) : 475490. doi: 10.3934/mcrf.2018019 
[2] 
Rohit Gupta, Farhad Jafari, Robert J. Kipka, Boris S. Mordukhovich. Linear openness and feedback stabilization of nonlinear control systems. Discrete & Continuous Dynamical Systems  S, 2018, 11 (6) : 11031119. doi: 10.3934/dcdss.2018063 
[3] 
Russell Johnson, Carmen Núñez. Remarks on linearquadratic dissipative control systems. Discrete & Continuous Dynamical Systems  B, 2015, 20 (3) : 889914. doi: 10.3934/dcdsb.2015.20.889 
[4] 
Jianhui Huang, Xun Li, Jiongmin Yong. A linearquadratic optimal control problem for meanfield stochastic differential equations in infinite horizon. Mathematical Control & Related Fields, 2015, 5 (1) : 97139. doi: 10.3934/mcrf.2015.5.97 
[5] 
Kai Du, Jianhui Huang, Zhen Wu. Linear quadratic meanfieldgame of backward stochastic differential systems. Mathematical Control & Related Fields, 2018, 8 (3&4) : 653678. doi: 10.3934/mcrf.2018028 
[6] 
Galina Kurina, Sahlar Meherrem. Decomposition of discrete linearquadratic optimal control problems for switching systems. Conference Publications, 2015, 2015 (special) : 764774. doi: 10.3934/proc.2015.0764 
[7] 
Zhenyu Lu, Junhao Hu, Xuerong Mao. Stabilisation by delay feedback control for highly nonlinear hybrid stochastic differential equations. Discrete & Continuous Dynamical Systems  B, 2019, 24 (8) : 40994116. doi: 10.3934/dcdsb.2019052 
[8] 
CătălinGeorge Lefter, ElenaAlexandra Melnig. Feedback stabilization with one simultaneous control for systems of parabolic equations. Mathematical Control & Related Fields, 2018, 8 (3&4) : 777787. doi: 10.3934/mcrf.2018034 
[9] 
Sigurdur Hafstein, Skuli Gudmundsson, Peter Giesl, Enrico Scalas. Lyapunov function computation for autonomous linear stochastic differential equations using sumofsquares programming. Discrete & Continuous Dynamical Systems  B, 2018, 23 (2) : 939956. doi: 10.3934/dcdsb.2018049 
[10] 
Nguyen Dinh Cong, Nguyen Thi Thuy Quynh. Coincidence of Lyapunov exponents and central exponents of linear Ito stochastic differential equations with nondegenerate stochastic term. Conference Publications, 2011, 2011 (Special) : 332342. doi: 10.3934/proc.2011.2011.332 
[11] 
Xingwu Chen, Jaume Llibre, Weinian Zhang. Averaging approach to cyclicity of hopf bifurcation in planar linearquadratic polynomial discontinuous differential systems. Discrete & Continuous Dynamical Systems  B, 2017, 22 (10) : 39533965. doi: 10.3934/dcdsb.2017203 
[12] 
Janusz Mierczyński, Sylvia Novo, Rafael Obaya. Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations. Communications on Pure & Applied Analysis, 2020, 19 (4) : 22352255. doi: 10.3934/cpaa.2020098 
[13] 
Hongyan Yan, Yun Sun, Yuanguo Zhu. A linearquadratic control problem of uncertain discretetime switched systems. Journal of Industrial & Management Optimization, 2017, 13 (1) : 267282. doi: 10.3934/jimo.2016016 
[14] 
Guangjun Shen, Xueying Wu, Xiuwei Yin. Stabilization of stochastic differential equations driven by GLévy process with discretetime feedback control. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020133 
[15] 
Tyrone E. Duncan. Some linearquadratic stochastic differential games for equations in Hilbert spaces with fractional Brownian motions. Discrete & Continuous Dynamical Systems  A, 2015, 35 (11) : 54355445. doi: 10.3934/dcds.2015.35.5435 
[16] 
Shigeaki Koike, Hiroaki Morimoto, Shigeru Sakaguchi. A linearquadratic control problem with discretionary stopping. Discrete & Continuous Dynamical Systems  B, 2007, 8 (2) : 261277. doi: 10.3934/dcdsb.2007.8.261 
[17] 
M. S. Mahmoud, P. Shi, Y. Shi. $H_\infty$ and robust control of interconnected systems with Markovian jump parameters. Discrete & Continuous Dynamical Systems  B, 2005, 5 (2) : 365384. doi: 10.3934/dcdsb.2005.5.365 
[18] 
Yanqing Liu, Yanyan Yin, Kok Lay Teo, Song Wang, Fei Liu. Probabilistic control of Markov jump systems by scenario optimization approach. Journal of Industrial & Management Optimization, 2019, 15 (3) : 14471453. doi: 10.3934/jimo.2018103 
[19] 
Lars Grüne, Peter E. Kloeden, Stefan Siegmund, Fabian R. Wirth. Lyapunov's second method for nonautonomous differential equations. Discrete & Continuous Dynamical Systems  A, 2007, 18 (2&3) : 375403. doi: 10.3934/dcds.2007.18.375 
[20] 
Eduardo Liz, Gergely Röst. On the global attractor of delay differential equations with unimodal feedback. Discrete & Continuous Dynamical Systems  A, 2009, 24 (4) : 12151224. doi: 10.3934/dcds.2009.24.1215 
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