A Negative Bendixson-Like Criterion for a Class of Hybrid Systems

Alexander Pogromsky, Henk Nijmeijer, Jacobus Rooda
2007 IEEE Transactions on Automatic Control  
A condition which ensures the absence of periodic orbits for nonsmooth dynamical systems is presented. The condition is a higher dimensional generalization of Bendixson's criterion applicable to differential inclusions that are useful in the description of hybrid systems. The main argument is based on contraction analysis of the -measured volume along the system trajectories. A connection to methods for estimating the Hausdorff dimension is emphasized. For a class of hybrid systems described by
more » ... ystems described by a linear system with relay feedback the conditions are presented in the form of linear matrix inequalities. A simple but illustrative example is analyzed. . His research fields of interest are modeling and analysis of manufacturing systems. His interest is especially in control of manufacturing lines and in supervisory control of manufacturing machines. Authorized licensed use limited to: IEEE Xplore. Downloaded on December 9, 2008 at 05:36 from IEEE Xplore. Restrictions apply.
doi:10.1109/tac.2007.894508 fatcat:pqy5xw6akjanrhbb46o76y23j4