@article {34, title = {Hybrid dynamical systems}, journal = {IEEE Control Systems Magazine}, volume = {29}, number = {2}, year = {2009}, month = {April}, pages = {28-93}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=4806347\&isnumber=4806311}, url = {https://hybrid.soe.ucsc.edu/files/preprints/34.pdf}, author = {R. Goebel and R. G. Sanfelice and A.R. Teel} } @article {29, title = {Generalized solutions to hybrid dynamical systems}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, volume = {14}, number = {4}, year = {2008}, pages = {699{\textendash}724}, abstract = {Several recent results in the area of robust asymptotic stability of hybrid systems show that the concept of a generalized solution to a hybrid system is suitable for the analysis and design of hybrid control systems. In this paper, we show that such generalized solutions are exactly the solutions that arise when measurement noise in the system is taken into account.}, keywords = {hybrid systems}, doi = {http://www.esaim-cocv.org/action/displayAbstract?fromPage=online\&aid=8133135\&fulltextType=RA\&doiId=S1292811908000080}, url = {https://hybrid.soe.ucsc.edu/files/preprints/29.pdf}, author = {R. G. Sanfelice and R. Goebel and A.R. Teel} } @conference {16, title = {Complex hybrid systems: stability analysis for omega limit sets}, booktitle = {Proc. 26th Chinese Control Conference}, series = {NULL}, year = {2007}, abstract = {This paper focuses on the asymptotic stability properties of omega limit sets for complex hybrid dynamical systems, which are commonly found in systems and engineering. It spells out specific stability results that follow when a hybrid dynamical system has certain structure, e.g., when it admits a decomposition resembling a cascade of hybrid dynamical systems.}, keywords = {hybrid systems}, url = {https://hybrid.soe.ucsc.edu/files/preprints/16.pdf}, author = {C. Cai and R. Goebel and R. G. Sanfelice and A.R. Teel} } @conference {15, title = {Hybrid systems techniques for convergence of solutions to switched systems}, booktitle = {Proc. 46th IEEE Conference on Decision and Control}, series = {NULL}, year = {2007}, pages = {92{\textendash}96}, abstract = {Invariance principles for hybrid systems are used to derive invariance principles for nonlinear switching systems with multiple Lyapunov-like functions. Dwell-time, persistent dwell-time, and weak dwell-time solutions are considered. Asymptotic stability results are deduced under observability assumptions or common bounds on the Lyapunov-like functions.}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=4435008\&isnumber=4434000}, url = {https://hybrid.soe.ucsc.edu/files/preprints/15.pdf}, author = {R. Goebel and R. G. Sanfelice and A.R. Teel} } @conference {6, title = {A feedback control motivation for generalized solutions to hybrid systems}, booktitle = {Hybrid Systems: Computation and Control, Lecture Notes in Computer Science 3927}, series = {NULL}, year = {2006}, pages = {522{\textendash}536}, publisher = {Springer Berlin / Heidelberg}, organization = {Springer Berlin / Heidelberg}, abstract = {

Several recent results in the area of robust asymptotic stability of hybrid systems show that the concept of a generalized solution to a hybrid system is suitable for the analysis and design of hybrid control systems. In this paper, we show that such generalized solutions are exactly the solutions that arise when measurement noise is present in the system.

}, keywords = {hybrid systems}, doi = {http://www.springerlink.com/content/p1l0517700517248/fulltext.pdf}, url = {https://hybrid.soe.ucsc.edu/files/preprints/6.pdf}, author = {R. G. Sanfelice and R. Goebel and A.R. Teel}, editor = {J. P. Hespanha and A. Tiwari and J. P. Hespanha and A. Tiwari} } @conference {4, title = {Results on convergence in hybrid systems via detectability and an invariance principle}, booktitle = {Proc. 24th American Control Conference}, series = {NULL}, year = {2005}, pages = {551{\textendash}556}, abstract = {

Two invariance principles for generalized hybrid systems are presented. One version involves the use of a nonincreasing function, like in the original work of LaSalle. The other version involves {\textquoteleft}{\textquoteleft}meagreness" conditions. These principles characterize asymptotic convergence of bounded hybrid trajectories to weakly invariant sets. A detectability property is used to locate a set in which the Omega-limit set of a trajectory is contained. Next, it is shown how the invariance principles can be used to certify asymptotic stability in hybrid systems. Lyapunov and Krasovskii theorems for hybrid systems are included.

}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/iel5/9861/31519/01470014.pdf?tp=\&arnumber=1470014\&isnumber=31519}, url = {https://hybrid.soe.ucsc.edu/files/preprints/4.pdf}, author = {R. G. Sanfelice and R. Goebel and A.R. Teel} } @conference {3, title = {Hybrid systems: generalized solutions and robust stability}, booktitle = {Proc. 6th IFAC Symposium in Nonlinear Control Systems}, series = {NULL}, year = {2004}, pages = {1{\textendash}12}, abstract = {

Robust asymptotic stability for hybrid systems is considered. For this purpose, a generalized solution concept is developed. The first step is to characterize a hybrid time domain that permits an efiient description of the convergence of a sequence of solutions. Graph convergence is used. Then a generalized solution definition is given that leads to continuity with respect to initial conditions and perturbations of the system data. This property enables new results on necessary conditions for asymptotic stability in hybrid systems.

}, keywords = {hybrid systems}, doi = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.61.8882\&rep=rep1\&type=pdf}, url = {https://hybrid.soe.ucsc.edu/files/preprints/3.pdf}, author = {R. Goebel and J.P. Hespanha and A.R. Teel and C. Cai and R. G. Sanfelice} }