Necessary and sufficient conditions for global asymptotic stability of a class of bimodal systems with discontinuous vector fields

[1]  Jun-ichi Imura,et al.  Characterization of well-posedness of piecewise-linear systems , 2000, IEEE Trans. Autom. Control..

[2]  John S. Spraker.  A Comparison of the Carathéodory and Filippov Solution Sets , 1996 .

[3]  Michael Margaliot,et al.  Stability Analysis of Second-Order Switched Homogeneous Systems , 2002, SIAM J. Control. Optim..

[4]  Bo Hu,et al.  Towards a stability theory of general hybrid dynamical systems , 1999, Autom..

[5]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[6]  Shinji Hara,et al.  Stability tests and stabilization for piecewise linear systems based on poles and zeros of subsystems , 2006, Autom..

[7]  Zhendong Sun,et al.  Stability of piecewise linear systems revisited , 2010, Annu. Rev. Control..

[8]  J. Cortés.  Discontinuous dynamical systems , 2008, IEEE Control Systems.

[9]  Enrique Ponce,et al.  Bifurcation of Invariant cones in Piecewise Linear Homogeneous Systems , 2005, Int. J. Bifurc. Chaos.

[10]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[11]  Vasfi Eldem,et al.  Well posedness conditions for Bimodal Piecewise Affine Systems , 2015, Syst. Control. Lett..

[12]  M. Kanat Camlibel,et al.  On the existence, uniqueness and nature of Carathéodory and Filippov solutions for bimodal piecewise affine dynamical systems , 2012, Syst. Control. Lett..

[13]  Enrique Ponce,et al.  The continuous matching of two stable linear systems can be unstable , 2006 .

[14]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Short Survey of Recent Results , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

[15]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[16]  P. Curran,et al.  A unifying framework for the circle criterion and other quadratic stability criteria , 2003, 2003 European Control Conference (ECC).

[17]  Robert Shorten,et al.  Stability Criteria for Switched and Hybrid Systems , 2007, SIAM Rev..

[18]  Isil Öner,et al.  A note on the stability of bimodal systems in with discontinuous vector fields , 2015, Int. J. Control.

[19]  Yasuaki Kuroe,et al.  A solution to the common Lyapunov function problem for continuous-time systems , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[20]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.