Abstract:
This paper is concerned with a qualitative method for the study of reachable sets and controllability of bilinear time-invariant systems. A nonlinear decomposition techni...Show MoreMetadata
Abstract:
This paper is concerned with a qualitative method for the study of reachable sets and controllability of bilinear time-invariant systems. A nonlinear decomposition technique which reduces the solution of the problem to the analysis of the qualitative behavior of a finite number of linear uncontrolled systems is introduced. Special consideration is given to the homogeneous bilinear systems with commutative matrices. Two- and three-dimensional examples are discussed.
Published in: IEEE Transactions on Automatic Control ( Volume: 41, Issue: 9, September 1996)
DOI: 10.1109/9.536506
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Cites in Papers - IEEE (14)
Select All
1.
Xing Wang, Bo Li, Jr-Shin Li, Ian R. Petersen, Guodong Shi, "Controllability and Accessibility on Graphs for Bilinear Systems Over Lie Groups", IEEE Transactions on Automatic Control, vol.68, no.4, pp.2277-2292, 2023.
2.
Lin Tie, "Controllability of Continuous-Time Bilinear Systems Without Using the Lie-Algebraic Conditions: A New Perspective", IEEE Transactions on Automatic Control, vol.68, no.4, pp.2094-2108, 2023.
3.
Xing Wang, Bo Li, Jr-Shin Li, Ian R. Petersen, Guodong Shi, "Graphical Characterizations for Structural Controllability of Drifted Bilinear Systems", 2021 60th IEEE Conference on Decision and Control (CDC), pp.5532-5537, 2021.
4.
Xing Wang, Bo Li, Jr-Shin Li, Ian R. Petersen, Guodong Shi, "Controllability over Graphs for Bilinear Systems over Lie Groups", 2020 59th IEEE Conference on Decision and Control (CDC), pp.5580-5585, 2020.
5.
Shu Lin, Bart De Schutter, Dewei Li, "Stabilizing Controller Design for State-Based Switching Bilinear Systems", 2018 IEEE Conference on Decision and Control (CDC), pp.6452-6457, 2018.
6.
Xian Zhang, Xin-Rong Yang, "Globally Exponentially Stabilizing Control for a Class of Continuous-Time Bilinear Systems", 2008 International Conference on Intelligent Computation Technology and Automation (ICICTA), vol.1, pp.359-363, 2008.
7.
Qi Yiwen, Zhang Xian, "Globally Asymptotically Stabilizing Control for a Class of Discrete-time Bilinear Systems", 2007 Chinese Control Conference, pp.309-311, 2007.
8.
Francesco Amato, Carlo Cosentino, Alessio Merola, "Stabilization of bilinear systems via linear state feedback control", 2007 Mediterranean Conference on Control & Automation, pp.1-5, 2007.
9.
Jiangbo Liu, Daizhan Cheng, "Accessibility Lie algebra of switched bilinear systems", 2005 International Conference on Control and Automation, vol.1, pp.65-70 Vol. 1, 2005.
10.
Daizhan Cheng, J.B. Liu, "On controllability of switched bilinear systems", Proceedings of the 2005, American Control Conference, 2005., pp.5109-5114 vol. 7, 2005.
11.
Daizhan Cheng, "Controllability of switched bilinear systems", IEEE Transactions on Automatic Control, vol.50, no.4, pp.511-515, 2005.
12.
Guoping Lu, D.W.C. Ho, Yufan Zheng, "Stabilization for singular bilinear systems", Proceedings of the 2004 American Control Conference, vol.2, pp.1049-1054 vol.2, 2004.
13.
Guoping Lu, Yufan Zheng, C. Zhang, Xinghuo Yu, "Global asymptotic stabilization of MIMO bilinear systems with undamped natural response", Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171), vol.2, pp.1989-1994 vol.2, 1998.
14.
A.Y. Khapalov, R.R. Mohler, "Global controllability of the power transmission network", Proceedings of 35th IEEE Conference on Decision and Control, vol.3, pp.3400-3405 vol.3, 1996.
Cites in Papers - Other Publishers (9)
1.
Shu Lin, Dewei Li, Bart Schutter, "Optimizing the performance of the feedback controller for state?based switching bilinear systems", Optimal Control Applications and Methods, vol.41, no.6, pp.1844, 2020.
2.
Francesco Carravetta, "Global Exact Quadratization of Continuous-Time Nonlinear Control Systems", SIAM Journal on Control and Optimization, vol.53, no.1, pp.235, 2015.
3.
Luis Alberto Fernández, Alexander Yuri Khapalov, "Controllability properties for the one-dimensional Heat equation under multiplicative or nonnegative additive controls with local mobile support", ESAIM: Control, Optimisation and Calculus of Variations, vol.18, no.4, pp.1207, 2012.
4.
Guoping Lu, Yufan Zheng, Cishen Zhang, "Dynamical Output Feedback Stabilization Of Mimo Bilinear Systems With Undamped Natural Response", Asian Journal of Control, vol.5, no.2, pp.251, 2008.
5.
A. Y. Khapalov, "Controllability of the Semilinear Parabolic Equation Governed by a Multiplicative Control in the Reaction Term: A Qualitative Approach", SIAM Journal on Control and Optimization, vol.41, no.6, pp.1886, 2003.
6.
Ronald R. Mohler, Encyclopedia of Physical Science and Technology, pp.659, 2003.
7.
Alexander Khapalov, Control Of Nonlinear Distributed Parameter Systems, 2001.
8.
R. R. Mohler, A. Y. Khapalov, "Bilinear Control and Application to Flexible a.c. Transmission Systems", Journal of Optimization Theory and Applications, vol.105, no.3, pp.621, 2000.
9.
A.Y. Khapalov, R.R. Mohler, "Asymptotic stabilization of the bilinear time-invariant system via piecewise-constant feedback", Systems & Control Letters, vol.33, no.1, pp.47, 1998.