Keywords: hybrid systems; non-smooth dynamical systems; discontinuity mappings; chattering-free simulation; numerical methods
Proceedings of the 56th Conference on Simulation and Modelling (SIMS 56), October, 7-9, 2015, Linköping University, Sweden
Myron Allen and Eli Isaacson. Numerical analysis for applied science. John Wiley and Sons, 1998.
Klaus-Jürgen Bathe and Gunwoo Noh. Insight into an implicit time integration scheme for structural dynamics. Computers and Structures, 2012.
Albert Benveniste, Timothy Bourke, Benoit Caillaud, and Marc Pouzet. Non-standard semantics of hybrid systems modelers. Journal of Computer and System Sciences, 2012.
Martin Biák, Tomáš Hanus, and Drahoslava Janovská. Some applications of filippov’s dynamical systems. Journal of Computational and Applied Mathematics, 2013.
John Charles Butcher. Numerical methods for ordinary differential equations. John Wiley and Sons, 2008.
Chaohong Cai, Rafal Goebel, Ricardo Sanfelice, and Andrew Teel. Hybrid systems: limit sets and zero dynamics with a view toward output regulation. Springer-Verilag, 2007.
François Cellier and Ernesto Kofman. Continuous system simulation. Springer Verlag, 2006.
Mario di Bernardo, Chris Budd, Alan Champneys, Piotr Kowalczyk, Arne Nordmark, Gerard Olivar Tost, and Petri Piiroinen. Bifurcations in nonsmooth dynamical systems. Industrial and Applied Mathematics, 2008.
Aleksei Fedorovich Filippov. Differential equations with discontinuous right-hand sides. Mathematics and its Applications, Kluwer Academic, 1988.
Marcel Guardia, Tere Seara, and Marco Antonio Teixeira. Generic bifurcations of low codimension of planar filippov systems. Journal of Differential Equations, 2011.
Karl Henrik Johansson, Andrey Barabanov, and Karl Johan Åström. Limit cycles with chattering in relay feedback systems. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 47(9), 2002.
Autar Kaw and Egwu Eric Kalu. Numerical methods with applications (1st edition). WordPress., 2008.
Hai Lin and Panos J. Antsaklis. Hybrid dynamical systems: Stability and stabilization. The Control Systems Handbook, Second Edition: Control System Advanced Methods. CRC Press, 2009.
Ben Morris. Hybrid invariant manifolds in systems with impulse effects with application to periodic locomotion in bipedal robots. IEEE Transactions on Automatic Control, 2009.
Claus-Dieter Munz, Florian Hindenlang, and Gregor Gassner. A runge-kutta based discontinuous galerkin method with time accurate local time stepping. Numerical Methods for Hyperbolic Equations: Theory an Applications., 2011.
Peter Schrammel. Logico-Numerical Verification Methods for Discrete and Hybrid Systems. PhD disseretation, 2012.
Vadim Utkin. Sliding mode in control and optimization. Springer, Berlin, 1992.
Daniel Weiss, Tassilo Küpper, and Hany Hosham. Invariant manifolds for nonsmooth systems with sliding mode. Mathematics and Computers in Simulation, 2014.
Fu Zhang, Murali Yeddanapudi, and Pieter Mosterman. Zerocrossing location and detection algorithms for hybrid system simulation. IFAC W. Cong., 2008.
Jun Zhang, Karl Henrik Johansson, John Lygeros, and Shankar Sastry. Zeno hybrid systems. International Journal of Robust and Nonlinear Control, 2001.