@article {18, title = {Invariance principles for hybrid systems with connections to detectability and asymptotic stability}, journal = {IEEE Transactions on Automatic Control}, volume = {52}, number = {12}, year = {2007}, pages = {2282{\textendash}2297}, abstract = {The paper shows several versions of the (LaSalle{\textquoteright}s) invariance principle for general hybrid systems. The broad framework allows for nonuniqueness of solutions, Zeno behaviors, and does not insist on continuous dependence of solutions on initial conditions. Instead, only a mild structural property involving graphical convergence of solutions is posed. The general invariance results are then specified to hybrid systems given by set-valued data. Further results involving invariance as well as observability, detectability, and asymptotic stability are given.}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=04395187}, url = {https://hybrid.soe.ucsc.edu/files/preprints/18.pdf}, author = {R. G. Sanfelice and R. Goebel and A. R. Teel} }