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Original Articles

Common quadratic Lyapunov-like functions with associated switching regions for two unstable second-order LTI systems

Pages 1127-1135 | Published online: 08 Nov 2010

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H. Ethabet, T. Raïssi, M. Amairi, C. Combastel & M. Aoun. (2020) Interval observer design for continuous-time switched systems under known switching and unknown inputs. International Journal of Control 93:5, pages 1088-1101.
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Shiming Duan, Jun Ni & A. Galip Ulsoy. (2012) An improved LMI-based approach for stability of piecewise affine time-delay systems with uncertainty. International Journal of Control 85:9, pages 1218-1234.
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A. Bacciotti & F. Ceragioli. (2006) Closed loop stabilization of planar bilinear switched systems. International Journal of Control 79:1, pages 14-23.
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Guisheng Zhai & Hai Lin. (2004) Controller failure time analysis for symmetric control systems. International Journal of Control 77:6, pages 598-605.
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Zhendong Sun. (2004) A robust stabilizing law for switched linear systems. International Journal of Control 77:4, pages 389-398.
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Zhen Wu, Yan Shi, Zhongyang Fei & Xiaofeng Liu. (2024) Mode-Recovered Bumpless Transfer Control for Aeroengines With Switched Models. IEEE Transactions on Aerospace and Electronic Systems 60:2, pages 2183-2192.
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Haifa Ethabet, Leila Dadi, Tarek Raïssi & Mohamed Aoun. (2023) L ∞ Set-membership Estimation for Continuous-time Switched Linear Systems . L ∞ Set-membership Estimation for Continuous-time Switched Linear Systems .
Leila Dadi, Haifa Ethabet & Mohamed Aoun. 2023. State Estimation and Stabilization of Nonlinear Systems. State Estimation and Stabilization of Nonlinear Systems 123 145 .
Zhongyang Fei, Liu Yang, Xi-Ming Sun & Shunqing Ren. (2022) Zonotopic Set-Membership State Estimation for Switched Systems With Restricted Switching. IEEE Transactions on Automatic Control 67:11, pages 6127-6134.
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Jun Huang, Haochi Che, Hieu Trinh, Xudong Zhao & Yueyuan Zhang. (2022) Functional interval estimation method for discrete-time switched systems under asynchronous switching. Journal of the Franklin Institute 359:11, pages 5712-5732.
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Jorge Davila, Tarek Raissi & Xubin Ping. (2021) A Collaborative Observer for Switched Linear Systems with Unknown Inputs. A Collaborative Observer for Switched Linear Systems with Unknown Inputs.
Jun Huang, Xiang Ma, Haochi Che & Zhengzhi Han. (2020) Further Result on Interval Observer Design for Discrete-Time Switched Systems and Application to Circuit Systems. IEEE Transactions on Circuits and Systems II: Express Briefs 67:11, pages 2542-2546.
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Awais Khan, Wei Xie & Long-Wen Liu. (2020) Set-Membership Interval State Estimator Design Using Observability Matrix for Discrete-Time Switched Linear Systems. IEEE Sensors Journal 20:11, pages 6121-6129.
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Xiang Ma, Jun Huang & Liang Chen. (2019) Finite-Time Interval Observers’ Design for Switched Systems. Circuits, Systems, and Signal Processing 38:11, pages 5304-5322.
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Haifa Ethabet, Tarek Raissi, Messaoud Amairi & Mohamed Aoun. (2019) Set-Membership Fault Detection for Continuous-time Switched Linear Systems. Set-Membership Fault Detection for Continuous-time Switched Linear Systems.
Jun Huang, Shanen Yu, Xiang Ma & Liang Chen. 2019. Positive Systems. Positive Systems 73 82 .
Minghui Chu, Jizheng Chu & Chi Xu. (2018) Graphical PID Controller Tuning Method for Parameter Uncertain System. Graphical PID Controller Tuning Method for Parameter Uncertain System.
Haifa Ethabet, Djahid Rabehi, Denis Efimov & Tarek Raïssi. (2018) Interval estimation for continuous-time switched linear systems. Automatica 90, pages 230-238.
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Haifa Ethabet, Tarek Raissi, Messaoud Amairi & Mohamed Aoun. (2017) Interval observers design for continuous-time linear switched systems. IFAC-PapersOnLine 50:1, pages 6259-6264.
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Liying Zhu. (2014) Global stability analysis of two-dimensional LTI switched systems with saddle points. Global stability analysis of two-dimensional LTI switched systems with saddle points.
Carmen Pérez & Francisco Benítez. (2012) Switched convergence of second-order switched nonlinear systems. International Journal of Control, Automation and Systems 10:5, pages 920-930.
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Shiming Duan, Jun Ni & A. G. Ulsoy. (2012) Stability criteria for uncertain piecewise affine time-delay systems. Stability criteria for uncertain piecewise affine time-delay systems.
A. BacciottiL. Mazzi. (2009) From Artstein-Sontag theorem to the min-projection strategy. Transactions of the Institute of Measurement and Control 32:6, pages 571-581.
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Jizhong Wang, Changxue Zhang & Yuejin Zhang. (2010) Study on the Sliding Mode of the Planar Switched Systems. Study on the Sliding Mode of the Planar Switched Systems.
Tingshu Hu, Liqiang Ma & Zongli Lin. (2008) Stabilization of Switched Systems via Composite Quadratic Functions. IEEE Transactions on Automatic Control 53:11, pages 2571-2585.
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Jizhong Wang, Changxue Zhang & Yuqiang Wu. (2008) Study of Stabilising Strategies for Switched Linear Systems. Study of Stabilising Strategies for Switched Linear Systems.
Franco Blanchini & Carlo Savorgnan. (2008) Stabilizability of switched linear systems does not imply the existence of convex Lyapunov functions. Automatica 44:4, pages 1166-1170.
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Fei Long, Shumin Fei, Zhumu Fu, Shiyou Zheng & Wei Wei. (2008) control and quadratic stabilization of switched linear systems with linear fractional uncertainties via output feedback. Nonlinear Analysis: Hybrid Systems 2:1, pages 18-27.
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F. Long, S. Fei & S. Zheng. (2008) STATE FEEDBACK SINGULAR H ∞ CONTROL FOR SWITCHED LINEAR SYSTEMS. Control and Intelligent Systems 36:1.
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A. Bacciotti & L. Mazzi. (2007) Stability of dynamical polysystems via families of Liapunov functions. Nonlinear Analysis: Theory, Methods & Applications 67:7, pages 2167-2179.
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Tingshu Hu, Liqiang Ma & Zongli Lin. (2006) On Several Composite Quadratic Lyapunov Functions for Switched Systems. On Several Composite Quadratic Lyapunov Functions for Switched Systems.
Franco Blanchini & Carlo Savorgnan. (2006) Stabilizability of switched linear systems does not imply the existence of convex Lyapunov functions. Stabilizability of switched linear systems does not imply the existence of convex Lyapunov functions.
Zhijian Ji, Xiaoxia Guo, Long Wang & Guangming Xie. (2006) Robust H∞ Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach. Journal of Dynamic Systems, Measurement, and Control 128:3, pages 696-700.
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Francesca Ceragioli. (2006) Finite valued feedback laws and piecewise classical solutions. Nonlinear Analysis: Theory, Methods & Applications 65:5, pages 984-998.
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Xi-Ming Sun, G.M. Dimirovski & Jun Zhao. (2006) An LMI method for stabilizing second-order switched systems. An LMI method for stabilizing second-order switched systems.
Yew-Wen Liang, Yu-Huan Tan, Sheng-Dong Xu & Jia-Liang Chang. (2005) On existence and construction of stabilizing switching laws between two unstable linear systems. On existence and construction of stabilizing switching laws between two unstable linear systems.
Zhendong Sun & Shuzhi Sam Ge. 2005. Switched Linear Systems. Switched Linear Systems 57 116 .
Zhijian Ji & Long Wang. (2004) Disturbance attenuation of uncertain switched linear systems. Disturbance attenuation of uncertain switched linear systems.
Guisheng Zhai, Hai Lin, Xuping Xu & A.N. Michel. (2004) Stability analysis and design of switched normal systems. Stability analysis and design of switched normal systems.
Guisheng Zhai, Xinkai Chen, Ye Sun & A.N. Michel. (2003) ℒ/sub 2/ gain analysis for switched symmetric systems with time delay under arbitrary switching. ℒ/sub 2/ gain analysis for switched symmetric systems with time delay under arbitrary switching.
Guisheng Zhai, Hai Lin & P.J. Antsaklis. (2003) Controller failure time analysis for symmetric H∞ control systems. Controller failure time analysis for symmetric H∞ control systems.
Guisheng Zhai, S. Takai, A.N. Michel & Xuping Xu. (2002) Improving closed-loop stability of second-order LTI systems by hybrid static output feedback. Improving closed-loop stability of second-order LTI systems by hybrid static output feedback.

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