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Hybrid dynamical systems, i.e.
M. Aizerman and F. Gantmakher, “On the stability of periodic motions,” Journal of Applied Mathematics and Mechanics , vol. 22, no. 6, pp. 1065–1078, 1958
1958
Earlier work this paper cites.
P. R. Owen, “Saltation of uniform grains in air,” Journal of Fluid Mechanics , vol. 20, no. 2, pp. 225–242, 1964
1964
Earlier work this paper cites.
D. Giaouris, A. Elbkosh, S. Banerjee et al. , “Control of switching circuits using complete-cycle solution matrices,” in IEEE International Conference on Industrial Technology , 2006, pp. 1960–1965
1965
Earlier work this paper cites.
W. De Backer, “Jump conditions for sensitivity coefficients,” in Sensitivity Methods in Control Theory . Pergamon, 1966, pp. 168–175
1966
Earlier work this paper cites.
A. F. Filippov, Differential Equations with Discontinuous Righthand Sides . Springer, 1988
1988
Earlier work this paper cites.
M. H. Raibert, H. B. Brown Jr, M. Chepponis et al. , “Dynamically stable legged locomotion,” Massachusetts Inst. of Tech, Cambridge Artificial Intelligence Lab, Tech. Rep., 1989
1989
Earlier work this paper cites.
T. McGeer, “Passive dynamic walking,” Int. J. Robotics Res. , vol. 9, no. 2, pp. 62–82, 1990
1990
Earlier work this paper cites.
S. F. Bockman, “Lyapunov exponents for systems described by differential equations with discontinuous right-hand sides,” in American Control Conference . IEEE, 1991, pp. 1673–1678
1991
Earlier work this paper cites.
A. Mathai and S. B. Provost, Quadratic Forms in Random Variables . Marcel Dekker, Inc., 1992
1992
Earlier work this paper cites.
A. Back, J. M. Guckenheimer, and M. Myers, “A dynamical simulation facility for hybrid systems,” in Hybrid Systems , ser. Lecture Notes in Computer Science. Springer Berlin / Heidelberg, 1993, vol. 736
1993
Earlier work this paper cites.
P. C. Müller, “Calculation of Lyapunov exponents for dynamic systems with discontinuities,” Chaos, Solitons & Fractals , vol. 5, no. 9, pp. 1671–1681, 1995
1995
Earlier work this paper cites.
R. v. Schwerin, M. Winckler, and V. Schulz, “Parameter estimation in discontinuous descriptor models,” in IUTAM Symposium on Optimization of Mechanical Systems . Springer, 1996, pp. 269–276
1996
Earlier work this paper cites.
A. P. Ivanov, “The stability of periodic solutions of discontinuous systems that intersect several surfaces of discontinuity,” Journal of Applied Mathematics and Mechanics , vol. 62, no. 5, pp. 677–685, 1998
1998
Earlier work this paper cites.
P. I. Barton, R. J. Allgor, W. F. Feehery, and S. Galán, “Dynamic optimization in a discontinuous world,” Industrial and Engineering Chemistry Research , 1998
1998
Earlier work this paper cites.
W. Lohmiller and J.-J. E. Slotine, “On contraction analysis for non-linear systems,” Automatica , vol. 34, no. 6, pp. 683–696, 1998
1998
Earlier work this paper cites.
R. I. Leine and D. H. van Campen, “Fold bifurcations in discontinuous systems,” in International Design Engineering Technical Conferences and Computers and Information in Engineering Conference , vol. 19777. American Society of Mechanical Engineers, 1999, pp. 1423–1429
1999
Earlier work this paper cites.
S. Galán, W. F. Feehery, and P. I. Barton, “Parametric sensitivity functions for hybrid discrete/continuous systems,” Applied Numerical Mathematics , vol. 31, no. 1, pp. 17–47, 1999
1999
Earlier work this paper cites.
O. Von Stryk, “User’s guide for DIRCOL–a direct collocation method for the numerical solution of optimal control problems,” Technische Universitat Darmstadt, Tech. Rep., 1999
1999
Earlier work this paper cites.
I. A. Hiskens and M. A. Pai, “Trajectory sensitivity analysis of hybrid systems,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications , vol. 47, no. 2, pp. 204–220, 2000
2000
Earlier work this paper cites.
A. P. Ivanov, “Stability of periodic motions with impacts,” in Impacts in Mechanical Systems . Springer, 2000, pp. 145–187
2000
Earlier work this paper cites.
M. Kunze, “Lyapunov exponents for non-smooth dynamical systems,” Non-Smooth Dynamical Systems , pp. 63–140, 2000
2000
Earlier work this paper cites.
X. Wang and J. K. Hale, “On monodromy matrix computation,” Computer Methods in Applied Mechanics and Engineering , vol. 190, no. 18-19, pp. 2263–2275, 2001
2001
Earlier work this paper cites.
D. Sternad, M. Duarte, H. Katsumata, and S. Schaal, “Bouncing a ball: tuning into dynamic stability.” Journal of Experimental Psychology: Human Perception and Performance , vol. 27, no. 5, p. 1163, 2001
2001
Earlier work this paper cites.
R. Leine and D. Van Campen, “Discontinuous bifurcations of periodic solutions,” Mathematical and Computer Modelling , vol. 36, no. 3, pp. 259–273, 2002
2002
Earlier work this paper cites.
P. I. Barton and C. K. Lee, “Modeling, simulation, sensitivity analysis, and optimization of hybrid systems,” ACM Transactions on Modeling and Computer Simulation , vol. 12, no. 4, 2002
2002
Earlier work this paper cites.
X. Koutsoukos, J. Kurien, and F. Zhao, “Monitoring and diagnosis of hybrid systems using particle filtering methods,” in International Symposium on Mathematical Theory of Networks and Systems , 2002
2002
Earlier work this paper cites.
J. Lygeros, K. H. Johansson, S. N. Simic et al. , “Dynamical properties of hybrid automata,” IEEE Transactions on Automatic Control , vol. 48, no. 1, pp. 2–17, 2003
2003
Earlier work this paper cites.
R. Leine and H. Nijmeijer, Dynamics and Bifurcations of Non-Smooth Mechanical Systems . Springer, 2004
2004
Earlier work this paper cites.
I. Lopez, J. Busturia, and H. Nijmeijer, “Energy dissipation of a friction damper,” Journal of Sound and Vibration , vol. 278, no. 3, pp. 539–561, 2004
2004
Earlier work this paper cites.
S. J. Julier and J. K. Uhlmann, “Unscented filtering and nonlinear estimation,” Proceedings of the IEEE , vol. 92, no. 3, pp. 401–422, 2004
2004
Earlier work this paper cites.
——, “Bifurcation phenomena in non-smooth dynamical systems,” European Journal of Mechanics-A/Solids , vol. 25, no. 4, pp. 595–616, 2006
2006
Earlier work this paper cites.
C. Chicone, Ordinary Differential Equations with Applications . Springer, 2006
2006
Earlier work this paper cites.
G. Welch and G. Bishop, “An introduction to the Kalman filter,” University of North Carolina at Chapel Hill, Tech. Rep. 95–041, 1995, Updated: July 24, 2006
2006
Earlier work this paper cites.
S. Maity, D. Giaouris, S. Banerjee et al. , “Control of bifurcations in power electronic DC-DC converters through manipulation of the saltation matrix,” in Proc. PhysCon , 2007, pp. 1–5
2007
Earlier work this paper cites.
D. Giaouris, S. Banerjee, B. Zahawi, and V. Pickert, “Stability analysis of the continuous-conduction-mode buck converter via Filippov’s method,” IEEE Transactions on Circuits and Systems I: Regular Papers , vol. 55, no. 4, pp. 1084–1096, 2008
2008
Earlier work this paper cites.
M. Di Bernardo, C. J. Budd, A. R. Champneys et al. , “Bifurcations in nonsmooth dynamical systems,” SIAM Review , vol. 50, no. 4, pp. 629–701, 2008
2008
Earlier work this paper cites.
M. Bernardo, C. Budd, A. R. Champneys, and P. Kowalczyk, Piecewise-Smooth Dynamical Systems: Theory and Applications . Springer Science & Business Media, 2008, vol. 163
2008
Earlier work this paper cites.
I. Daho, D. Giaouris, B. Zahawi et al. , “Stability analysis and bifurcation control of hysteresis current controlled Ćuk converter using Filippov’s method,” in 4th IET Conference on Power Electronics, Machines and Drives , 2008, pp. 381–385
2008
Earlier work this paper cites.
A. Elbkosh, D. Giaouris, V. Pickert et al. , “Stability analysis and control of bifurcations of parallel connected DC/DC converters using the monodromy matrix,” in IEEE International Symposium on Circuits and Systems , 2008, pp. 556–559
2008
Earlier work this paper cites.
A. Elbkosh, D. Giaouris, B. Zahawi et al. , “Control of bifurcation of DC/DC buck converters controlled by double-edged PWM waveform,” in European Nonlinear Oscillations Conference , 2008, pp. 1–5
2008
Earlier work this paper cites.
F. Pfeiffer and C. Glocker, Multibody Dynamics with Unilateral Contacts . Wiley, 2008
2008
Earlier work this paper cites.
R. Goebel, R. G. Sanfelice, and A. R. Teel, “Hybrid dynamical systems,” IEEE Control Systems Magazine , vol. 29, no. 2, pp. 28–93, 2009
2009
Earlier work this paper cites.
S. Banerjee, J. Ing, E. Pavlovskaia et al. , “Invisible grazings and dangerous bifurcations in impacting systems: The problem of narrow-band chaos,” Physical Review E , vol. 79, p. 037201, Mar 2009
2009
Earlier work this paper cites.
D. Giaouris, S. Maity, S. Banerjee et al. , “Application of Filippov method for the analysis of subharmonic instability in DC–DC converters,” International Journal of Circuit Theory and Applications , vol. 37, no. 8, pp. 899–919, 2009
2009
Earlier work this paper cites.
G. Schultz and K. Mombaur, “Modeling and optimal control of human-like running,” IEEE/ASME Transactions on mechatronics , vol. 15, no. 5, pp. 783–792, 2009
2009
Cited alongside, same era.
N. Okafor, D. Giaouris, B. Zahawi, and S. Banerjee, “Analysis of fast-scale instability in DC drives with full-bridge converter using Filippov’s method,” IET Conference Proceedings , pp. 235–235(1), 2010
2010
Cited alongside, same era.
M. Fečkan and M. Pospíšil, “On the bifurcation of periodic orbits in discontinuous systems,” Communications in Mathematical Analysis , vol. 8, no. 1, pp. 87–108, 2010
2010
Cited alongside, same era.
N. Okafor, B. Zahawi, D. Giaouris, and S. Banerjee, “Chaos, coexisting attractors, and fractal basin boundaries in DC drives with full-bridge converter,” in IEEE International Symposium on Circuits and Systems , 2010, pp. 129–132
2010
Cited alongside, same era.
H. Jiang, A. S. Chong, Y. Ueda, and M. Wiercigroch, “Grazing-induced bifurcations in impact oscillators with elastic and rigid constraints,” International Journal of Mechanical Sciences , vol. 127, pp. 204–214, 2017
2017
Later among the works it cites.
S. Nobukawa, H. Nishimura, and T. Yamanishi, “Chaotic resonance in typical routes to chaos in the Izhikevich neuron model,” Scientific Reports , vol. 7, no. 1, pp. 1–9, 2017
2017
Later among the works it cites.
A. Abusorrah, K. Mandal, D. Giaouris et al. , “Avoiding instabilities in power electronic systems: Toward an on-chip implementation,” IET Power Electronics , vol. 10, no. 13, pp. 1778–1787, 2017
2017
Later among the works it cites.
A. El Aroudi, M. S. Al-Numay, W. G. Lu et al. , “A combined analytical-numerical methodology for predicting subharmonic oscillation in H-bridge inverters under double edge modulation,” IEEE Transactions on Circuits and Systems I: Regular Papers , vol. 65, no. 7, pp. 2341–2351, 2017
2017
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A. Ageno and A. Sinopoli, “Lyapunov’s Exponents for Non-Smooth Dynamical Systems: Behavior Identification Across Stability Boundaries With Bifurcations,” in International Conference on Multibody Systems, Nonlinear Dynamics, and Control , 09 2005, pp. 1999–2010
2010
Cited alongside, same era.
P. Kowalczyk and P. Glendinning, “Micro-chaos in relay feedback systems with bang-bang control and digital sampling,” IFAC Proceedings Volumes , vol. 44, no. 1, pp. 13 305–13 310, 2011
2011
Cited alongside, same era.
F. Bizzarri, A. Brambilla, S. Perticaroli, and G. S. Gajani, “Noise in a phase-quadrature pulsed energy restore oscillator,” in IEEE European Conference on Circuit Theory and Design , 2011, pp. 465–468
2011
Cited alongside, same era.
D. Giaouris, S. Banerjee, O. Imrayed et al. , “Complex interaction between tori and onset of three-frequency quasi-periodicity in a current mode controlled boost converter,” IEEE Transactions on Circuits and Systems I: Regular Papers , vol. 59, no. 1, pp. 207–214, 2011
2011
Cited alongside, same era.
S. Banerjee, D. Giaouris, O. Imrayed et al. , “Nonsmooth dynamics of electrical systems,” in IEEE International Symposium of Circuits and Systems , 2011, pp. 2709–2712
2011
Cited alongside, same era.
F. Bizzarri, A. Brambilla, and G. S. Gajani, “Steady state computation and noise analysis of analog mixed signal circuits,” IEEE Transactions on Circuits and Systems I: Regular Papers , vol. 59, no. 3, pp. 541–554, 2011
2011
Cited alongside, same era.
C. Morel, D. Petreus, and A. Rusu, “Application of the Filippov method for the stability analysis of a photovoltaic system,” Advances in Electrical and Computer Engineeging , vol. 11, pp. 93–98, 2011
2011
Cited alongside, same era.
K. Chakrabarty and U. Kar, “Control of bifurcation of PWM controlled DC drives,” in IEEE International Conference on Power Electronics, Drives and Energy Systems , 2012, pp. 1–8
2012
Cited alongside, same era.
Later among the works it cites.
K. Mandal, A. Abusorrah, M. M. Al-Hindawi et al. , “Control-oriented design guidelines to extend the stability margin of switching converters,” in IEEE International Symposium on Circuits and Systems , 2017, pp. 1–4
2017
Later among the works it cites.
M. Rijnen, E. De Mooij, S. Traversaro et al. , “Control of humanoid robot motions with impacts: Numerical experiments with reference spreading control,” in IEEE International Conference on Robotics and Automation , 2017, pp. 4102–4107
2017
Later among the works it cites.
M. Rijnen, A. Saccon, and H. Nijmeijer, “Reference spreading trajectory tracking control: Experimental analysis on a one-degree-of-freedom setup,” in European Nonlinear Oscillations Conference , 2017, pp. 1–2
2017
Later among the works it cites.
M. Kelly, “An introduction to trajectory optimization: How to do your own direct collocation,” SIAM Review , vol. 59, no. 4, pp. 849–904, 2017
2017
Later among the works it cites.
A. M. Pace and S. A. Burden, “Piecewise-differentiable trajectory outcomes in mechanical systems subject to unilateral constraints,” in International Conference on Hybrid Systems: Computation and Control , 2017, pp. 243–252
2017
Later among the works it cites.
R. M. Murray, Z. Li, and S. S. Sastry, A Mathematical Introduction to Robotic Manipulation . CRC press, 2017
2017
Later among the works it cites.
S. Coombes, Y. M. Lai, M. Şayli, and R. Thul, “Networks of piecewise linear neural mass models,” European Journal of Applied Mathematics , vol. 29, no. 5, pp. 869–890, 2018
2018
Later among the works it cites.
Y. M. Lai, R. Thul, and S. Coombes, “Analysis of networks where discontinuities and nonsmooth dynamics collide: Understanding synchrony,” The European Physical Journal Special Topics , vol. 227, no. 10, pp. 1251–1265, 2018
2018
Later among the works it cites.
Y. Park, K. M. Shaw, H. J. Chiel, and P. J. Thomas, “The infinitesimal phase response curves of oscillators in piecewise smooth dynamical systems,” European Journal of Applied Mathematics , vol. 29, no. 5, pp. 905–940, 2018
2018
Later among the works it cites.
H. Asahara and T. Kousaka, “Stability analysis using monodromy matrix for impacting systems,” IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences , vol. 101, no. 6, pp. 904–914, 2018
2018
Later among the works it cites.
R. Nicks, L. Chambon, and S. Coombes, “Clusters in nonsmooth oscillator networks,” Physical Review E , vol. 97, no. 3, p. 032213, 2018
2018
Later among the works it cites.
A. El Aroudi, L. Benadero, E. Ponce et al. , “Nonlinear dynamic modeling and analysis of self-oscillating H-bridge parallel resonant converter under zero current switching control: Unveiling coexistence of attractors,” IEEE Transactions on Circuits and Systems I: Regular Papers , vol. 66, no. 4, pp. 1657–1667, 2018
2018
Later among the works it cites.
G. Gkizas, “Border collisions in interleaved multi-output DC-DC boost converters,” in International Symposium on Nonlinear Theory and Its Applications , 08 2018
2018
Later among the works it cites.
H. Wu, V. Pickert, X. Deng et al. , “Polynomial curve slope compensation for peak-current-mode-controlled power converters,” IEEE Transactions on Industrial Electronics , vol. 66, no. 1, pp. 470–481, 2018
2018
Later among the works it cites.
M. Rijnen, J. B. Biemond, N. Van De Wouw et al. , “Hybrid systems with state-triggered jumps: Sensitivity-based stability analysis with application to trajectory tracking,” IEEE Transactions on Automatic Control , vol. 65, no. 11, pp. 4568–4583, 2019
2019
Later among the works it cites.
D.-H. Chen, S.-X. Xie, X.-C. Huang, and Y.-M. Chen, “Calculating Floquet multipliers for periodic solution of non-smooth dynamical system,” in International Conference on Applied Mathematics, Modeling, Simulation, and Optimization , 2019, pp. 27–33
2019
Later among the works it cites.
J.-G. Muñoz, A. Pérez, and F. Angulo, “Enhancing the stability of the switched systems using the saltation matrix,” International Journal of Structural Stability and Dynamics , vol. 19, no. 05, p. 1941004, 2019
2019
Later among the works it cites.
S. Corner, C. Sandu, and A. Sandu, “Modeling and sensitivity analysis methodology for hybrid dynamical system,” Nonlinear Analysis: Hybrid Systems , vol. 31, pp. 19–40, 2019
2019
Later among the works it cites.
R. Mallik, A. M. Pace, S. A. Burden, and B. Johnson, “Accurate small–signal discrete–time model of dual active bridge using saltation matrices,” in IEEE Energy Conversion Congress and Exposition (ECCE) , 2020, pp. 6312–6317
2020
Later among the works it cites.
K. Chakrabarty and U. Kar, “Dynamic behavior of PWM controlled DC drive,” Scientific Voyage , vol. 1, no. 1, pp. 1–12, 2020
2020
Later among the works it cites.
A. El Aroudi, K. Mandal, M. S. Al-Numay et al. , “Piecewise quadratic slope compensation technique for DC-DC switching converters,” IEEE Transactions on Circuits and Systems I: Regular Papers , vol. 67, no. 12, pp. 5574–5585, 2020
2020
Later among the works it cites.
W. Yang and M. Posa, “Impact invariant control with applications to bipedal locomotion,” in IEEE/RSJ International Conference on Intelligent Robots and Systems , 2021, pp. 5151–5158
2021
Later among the works it cites.
N. J. Kong, J. J. Payne, G. Council, and A. M. Johnson, “The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems,” Automatica , vol. 131, p. 109752, 2021
2021
Later among the works it cites.
N. J. Kong, G. Council, and A. M. Johnson, “iLQR for piecewise-smooth hybrid dynamical systems,” in IEEE Conference on Decision and Control , December 2021, pp. 5374–5381
2021
Later among the works it cites.
L. Dieci and C. Elia, “Master stability function for piecewise smooth networks,” arXiv:10.48550 , 2021
2021
Later among the works it cites.
O. Kuznyetsov, “Calculation of stable and unstable periodic orbits in a chopper-fed DC drive,” Mathematical Modeling and Computing , vol. 8, no. 1, pp. 43–57, 2021
2021
Later among the works it cites.
J.-G. Muñoz, F. Angulo, and D. Angulo-Garcia, “Designing a hysteresis band in a boost flyback converter,” Mechanical Systems and Signal Processing , vol. 147, p. 107080, 2021
2021
Later among the works it cites.
Y. Gao and Y. Gu, “Invariant filtering for bipedal walking on dynamic rigid surfaces with orientation-based measurement model,” 2021
2021
Later among the works it cites.
A. M. Johnson, “Impacts,” in Advanced Robot Dynamics . Unpublished Notes, 2021. [Online]. Available: https://www.andrew.cmu.edu/user/amj1/book/
2021
Later among the works it cites.
2022
Later among the works it cites.
J. J. Payne, N. J. Kong, and A. M. Johnson, “The uncertainty aware Salted Kalman Filter: State estimation for hybrid systems with uncertain guards,” in IEEE/RSJ Intl. Conference on Intelligent Robots and Systems , October 2022
2022
Later among the works it cites.
J. Zhu, N. J. Kong, G. Council, and A. M. Johnson, “Hybrid event shaping to stabilize periodic hybrid orbits,” in IEEE Intl. Conference on Robotics and Automation , Philadelphia, PA, May 2022, pp. 6600–6606
2022
Later among the works it cites.
2022
Later among the works it cites.
2022
Later among the works it cites.
C. Morel, A. Akrad, R. Sehab et al. , “Open-circuit fault-tolerant strategy for interleaved boost converters via Filippov method,” Energies , vol. 15, no. 1, p. 352, 2022
2022
Later among the works it cites.
S. A. Burden and S. D. Coogan, “On infinitesimal contraction analysis for hybrid systems,” IEEE Conference on Decision and Control , 2022
2022
Later among the works it cites.
Y. Gao, C. Yuan, and Y. Gu, “Invariant filtering for legged humanoid locomotion on a dynamic rigid surface,” IEEE/ASME Transactions on Mechatronics , vol. 27, no. 4, pp. 1900–1909, 2022
2022
Later among the works it cites.
G. Council, S. Revzen, and S. A. Burden, “Representing and Computing the B-Derivative of the Piecewise-Differentiable Flow of a Class of Nonsmooth Vector Fields,” Journal of Computational and Nonlinear Dynamics , vol. 17, no. 9, 06 2022, 091004
2022
Later among the works it cites.
R. Tedrake, Underactuated Robotics . Course Notes for MIT 6.832, 2022. [Online]. Available: http://underactuated.mit.edu
2022
Later among the works it cites.
J. Zhu, J. J. Payne, and A. M. Johnson, “Convergent iLQR for safe trajectory planning and control of legged robots,” IEEE International Conference on Robotics and Automation , 2024
2024
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