@article {40,
	title = {Dynamical Properties of Hybrid Systems Simulators},
	journal = {Automatica},
	volume = {46},
	number = {2},
	year = {2010},
	pages = {239{\textendash}248},
	abstract = {This paper analyzes the dynamical properties of a class of hybrid systems simulators. A hybrid system is a dynamical system with a state that can both ?ow and jump. Its simulator attempts to generate its solutions approximately. The paper presents mild regularity conditions on the hybrid system and its simulator to guarantee that simulated solutions are close to actual solutions on compact (hybrid) time intervals, and that asymptotically stable compact sets are preserved, in a semiglobal practical sense, under simulation. In fact, it is established that asymptotically stable compact sets are continuous in the integration step size parameter of the simulator; that is, as the step size of the simulator converges to zero, the asymptotically stable set observed in simulations approaches the asymptotically stable compact set of the true hybrid system. Examples are used to illustrate concepts and results.},
	keywords = {simulation},
	doi = {http://www.sciencedirect.com/science/article/pii/S0005109809004361},
	url = {https://hybrid.soe.ucsc.edu/files/preprints/40.pdf},
	author = {R. G. Sanfelice and A. R. Teel}
}
@conference {8,
	title = {On the continuity of asymptotically stable compact sets for simulations of hybrid systems},
	booktitle = {Proc. 45th IEEE Conference on Decision and Control},
	series = {NULL},
	year = {2006},
	pages = {270{\textendash}275},
	abstract = {<p>We propose a hybrid model for simulations of hybrid systems and we establish conditions on its data so that the asymptotically stable sets observed in simulations are continuous. The most important components of the hybrid model for simulations are a discrete integration scheme for the computation of the flows and an approximated jump mapping for the computation of the jumps. Our main result is built on the facts that, on compact hybrid time domains, every simulation to a hybrid system is arbitrarily close (in the graphical sense) to some solution to the actual hybrid system, and that asymptotically stable compact sets of hybrid systems are semiglobally practically asymptotically stable compact sets for the hybrid model for simulations. We present these results and illustrate them in simulations of the bouncing ball system.</p>},
	keywords = {simulation},
	doi = {http://ieeexplore.ieee.org/iel5/4176992/4176993/04177840.pdf?tp=\&isnumber=4176993\&arnumber=4177840\&punumber=\%3Cb\%3E\%3Cfont\%20color=990000\%3E4176992\%3C/font\%3E\%3C/b\%3E:PDF},
	url = {https://hybrid.soe.ucsc.edu/files/preprints/8.pdf},
	author = {R. G. Sanfelice and A. R. Teel}
}
