Characterising the stabilisability for second-order linear switched systems

References

• Balde , M , Boscain , U and Mason , P . 2009 . A Note on Stability Conditions for Planar Switched Systems . International Journal of Control , 82 : 1882 – 1888 . doi: 10.1080/00207170902802992
   Web of Science ®Google Scholar
• Barabanov , N . 2005 . Lyapunov Exponent and Joint Spectral Radius: Some Known and New Results . Proceedings of the 44th IEEE Conference on Decision Control . 2005 . pp. 2332 – 2337 . Seville , , Spain
   Google Scholar
• Blanchini , F . 1999 . Set Invariance in Control . Automatica , 35 : 1747 – 1767 . doi: 10.1016/S0005-1098(99)00113-2
   Web of Science ®Google Scholar
• Blanchini , F , Colaneri , P and Valcher , ME . 2011 . Is Stabilisation of Switched Positive Linear Systems is Equivalent to the Existence of an Hurwitz Convex Combination of the System Matrices? . Proceedings of the 50th IEEE Conference on Decision Control . 2011 . pp. 1834 – 1839 . Orlando , , USA
   Google Scholar
• Blanchini , F and Savorgnan , C . 2008 . Stabilizability of Switched Linear Systems Does Not Imply the Existence of Convex Lyapunov Function . Automatica , 44 : 1166 – 1170 . doi: 10.1016/j.automatica.2007.08.012
   Web of Science ®Google Scholar
• Bolzern , P , Colaneri , P and Geromel , JC . 2007 . “ Optimal Switching of 1-DOF Oscillating Systems ” . In Hybrid Systems: Computation and Control , Edited by: Bemporad , A. , Bicchi , A. and Buttazzo , G. Vol. 4416 , 118 – 130 . Berlin : Springer . LNCS
   Google Scholar
• Chesi , G . 2009 . On the Minimum Stable Communication Time for Switching Nonlinear Systems . IEEE Transactions on Automatic Control , 54 : 1284 – 1289 . doi: 10.1109/TAC.2009.2013054
   Web of Science ®Google Scholar
• Cong , S and Yin , L-P . 2012 . Switching Control Approach to Exponential Stabilisation of Planar Bilinear Systems . IET Control Theory Applications , 6 : 1313 – 1318 . doi: 10.1049/iet-cta.2011.0366
   Web of Science ®Google Scholar
• Dayawansa , WP and Martin , CF . 1999 . A Converse Lyapunov Theorem for a Class of Dynamical Systems Which Undergo Switching . IEEE Transactions on Automatic Control , 44 : 751 – 760 . doi: 10.1109/9.754812
   Web of Science ®Google Scholar
• DeCarlo , RA , Branicky , MS , Pettersson , S and Lennartson , B . 2000 . Perspectives and Results on the Stability and Stabilisability of Hybrid Systems . Proceedings of the IEEE , 88 : 1069 – 1082 . doi: 10.1109/5.871309
   Web of Science ®Google Scholar
• Filippov , AF . 1980 . Stability Conditions in Homogeneous Systems with Arbitrary Regime Switching . Automation and Remote Control , 41 : 1078 – 1085 .
   Web of Science ®Google Scholar
• Geromel , JC and Colaneri , P . 2006 . Stability and Stabilisation of Continuous-time Switched Linear Systems . SIAM Journal of Control Optimization , 45 : 1915 – 1930 . doi: 10.1137/050646366
   Web of Science ®Google Scholar
• Holcman , D and Margaliot , M . 2003 . Stability Analysis of Second-order Switched Homogeneous Systems . SIAM Journal of Control Optimization , 41 : 1609 – 1625 . doi: 10.1137/S0363012901389354
   Web of Science ®Google Scholar
• Hu , T and Blanchini , F . 2010 . Non-conservative Matrix Inequality Conditions for Stability/Stabilisability of Linear Differential Inclusions . Automatica , 46 : 190 – 196 . doi: 10.1016/j.automatica.2009.10.022
   Web of Science ®Google Scholar
• Huang , ZH , Xiang , C , Lin , H and Lee , TH . 2010 . Necessary and Sufficient Conditions for Regional Stabilisability of Generic Switched Linear Systems with a Pair of Planar Subsystems . International Journal of Control , 83 : 694 – 715 . doi: 10.1080/00207170903384321
   Web of Science ®Google Scholar
• Lin , H and Antsaklis , PJ . 2007 . Switching Stabilisability for Continuous-time Uncertain Switched Linear Systems . IEEE Transactions on Automatic Control , 52 : 633 – 646 . doi: 10.1109/TAC.2007.894515
   Web of Science ®Google Scholar
• Lin , H and Antsaklis , PJ . 2009 . Stability and Stabilisability of Switched Linear Systems: A Survey of Recent Results . IEEE Transactions on Automatic Control , 54 : 308 – 322 . doi: 10.1109/TAC.2008.2012009
   Web of Science ®Google Scholar
• Margaliot , M . 2006 . Stability Analysis of Switched Systems using Variational Principles: An Introduction . Automatica , 42 : 2059 – 2077 . doi: 10.1016/j.automatica.2006.06.020
   Web of Science ®Google Scholar
• Margaliot , M and Branicky , MS . 2009 . Nice Reachability of Planar Bilinear Control Systems with Applications to Planar Linear Switched Systems . IEEE Transactions on Automatic Control , 54 : 1430 – 1435 . doi: 10.1109/TAC.2009.2022905
   Web of Science ®Google Scholar
• Margaliot , M and Langholz , G . 2003 . Necessary and Sufficient Conditions for Absolute Stability: the Case of Second-order Systems . IEEE Transactions on Circuits Systems I , 50 : 227 – 234 . doi: 10.1109/TCSI.2002.808219
   Web of Science ®Google Scholar
• Molchanov , AP and Pyatnitskiy , YS . 1989 . Criteria of Asymptotic Stability of Differential and Difference Inclusions Encountered in Control Theory . System Control and Letters , 13 : 59 – 64 . doi: 10.1016/0167-6911(89)90021-2
   Web of Science ®Google Scholar
• Pettersson , S . 2003 . Synthesis of Switched Linear Systems . Proceedings of the 42nd IEEE Conference on Decision Control . 2003 . pp. 5283 – 5288 . Maui , , USA
   Google Scholar
• Pyatnitskiy , ES and Rapoport , LB . 1996 . Criteria of Asymptotic Stability of Differential Inclusions and Periodic Motions of Time-varying Nonlinear Control Systems . IEEE Transactions on Circuits Systems I , 43 : 219 – 229 . doi: 10.1109/81.486446
   Web of Science ®Google Scholar
• Xu , X and Antsaklis , PJ . 2000 . Stabilization of Second-order LTI Switched Systems . International Journal of Control , 73 : 1261 – 1279 . doi: 10.1080/002071700421664
   Web of Science ®Google Scholar
• Yfoulis , CA . 2010 . Constrained Switching Stabilisation of Linear Uncertain Switched Systems using Piecewise Linear Lyapunov Functions . Transactions of the Institute of Measurement & Control , 32 : 529 – 566 . doi: 10.1177/0142331208097842
   Web of Science ®Google Scholar
• Zevin , AA and Pinsky , MA . 2011 . Optimal Exponential Stabilisation of Planar Systems . Automatica , 47 : 965 – 961 . doi: 10.1016/j.automatica.2011.01.051
   Web of Science ®Google Scholar