Publications
Research Metrics:
- MathSciNet subscribers can access reviews of my publications here.
- Citation Data (as of September 2022):
- Google Scholar: 69 papers covered; 1941 citations; h-index=21; i10-index=39.
- MathSciNet citation data: 48 papers reviewed; 628 citations by 410 unique authors; h-index=15.
Selected (recent) publications:
- J.M. Davis, P. Hagelstein, Gibbs phenomena for some classical orthogonal polynomials, Journal of Mathematical Analysis and Applications, 505 (2022), 1-14.
- B. Jackson, J.M. Davis, An ergodic approach to Laplace transforms on time scales, Journal of Mathematical Analysis and Applications, 502 (2021), 1-31.
- B. Jackson, J.M. Davis, D. Poulsen, A polar representation of the Hilger complex plane, International Journal of Difference Equations 15 (2020), 419-427.
- B. Jackson, J.M. Davis, An ergodic approach to Pötzsche-Siegmund-Wirth’s region of exponential stability, Nonlinear Anal. Hybrid Syst. 36 (2020), 1-17.
- D. Poulsen, J.M. Davis, I. Gravagne, Mean square stability for systems on stochastically generated discrete time scales, Nonlinear Anal. Hybrid Syst. 31 (2019), 41–55.
- D. Poulsen, J.M. Davis, I. Gravagne, The geometry of the region of uniform exponential stability for linear time invariant dynamic equations on time scales. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 25 (2018),159–173.
- J.M. Davis, G. Eisenbarth, Singular value conditions for stability of dynamic switched systems, Journal of Mathematical Analysis and Applications, 452 (2017), 814-829.
- M. Mosley, I. Gravagne, J. Davis, Experimental investigation of a time scales-based stability criterion over finite time horizons, Proceedings of ASME Dynamic Systems and Control, Columbus, OH, 2015.
- D. Poulsen, I. Gravagne, J. Davis, Numeric and analytic investigations of mean-square exponential stability for stochastically timed systems, Proceedings of ASME Dynamic Systems and Control, Columbus, OH, 2015.
- D. Poulsen, I. Gravagne, J. Davis, Is deterministic real-time control always necessary? A time scales perspective, Proceedings of ASME Dynamic Systems and Control, San Antonio, TX, 2014.
- G. Eisenbarth, J.M. Davis, I. Gravagne, Stability of simultaneously triangularizable switched systems on hybrid domains, Electronic Journal of Differential Equations 2014 (2014), 1-19.
- G. Eisenbarth, J.M. Davis, I.A. Gravagne, On common quadratic Lyapunov functions for dynamic normal switched systems, IEEE Proceedings of the 45th Meeting of the Southeastern Symposium on System Theory, Baylor University, March 11, 2013.
- D. Poulsen, J.M. Davis, I.A. Gravagne, Observer based feedback controllers on stochastic time scales, IEEE Proceedings of the 45th Meeting of the Southeastern Symposium on System Theory, Baylor University, March 11, 2013.
- D. Poulsen, J.M. Davis, I.A. Gravagne, Stochastic time scales: quadratic Lyapunov functions and probabilistic regions of stability, IEEE Proceedings of the 45th Meeting of the Southeastern Symposium on System Theory, Baylor University, March 11, 2013.
- I.A. Gravagne, J.M. Davis, D. Poulsen, Time scale-based observer design for battery state-of-charge estimation, IEEE Proceedings of the 44th Meeting of the Southeastern Symposium on System Theory, University of North Florida, March 11-13, 2012.
- D. Poulsen, J.M. Davis, I.A. Gravagne, R.J. Marks II, On the stability of mu-varying dynamic equations on stochastically generated time scales, IEEE Proceedings of the 44th Meeting of the Southeastern Symposium on System Theory, University of North Florida, March 11-13, 2012.
- J.J. DaCunha, J.M. Davis, A unified Floquet theory for discrete, continuous, and hybrid periodic linear systems, Journal of Differential Equations 251 (2011), 2987-3027.
- J.M. Davis and G. Eisenbarth, The Positivstellensatz and nonexistence of common quadratic Lyapunov functions, IEEE Proceedings of the 43rd Meeting of the Southeastern Symposium on System Theory, Auburn University, March 14-16, 2011.
- J.M. Davis, I.A. Gravagne, B.J. Jackson, R.J. Marks II, Regions of exponential stability for LTI systems on nonuniform domains, IEEE Proceedings of the 43rd Meeting of the Southeastern Symposium on System Theory, Auburn University, March 14-16, 2011.
- I.A. Gravagne, E. Johns, J.M. Davis, Switched linear systems on time scales with relaxed commutativity constraints, IEEE Proceedings of the 43rd Meeting of the Southeastern Symposium on System Theory, Auburn University, March 14-16, 2011.
- B.J. Jackson, J.M. Davis, I.A. Gravagne, R.J. Marks II, Linear state feedback stabilization on time scales, International Journal of Dynamical Systems and Differential Equations 3 (2011), 163–177. arXiv:0910.3034v1 [math.OC]
- J.M. Davis, I.A. Gravagne, B.J. Jackson, R.J. Marks II, State feedback stabilization of linear time-varying systems on time scales, IEEE Proceedings of the 42nd Meeting of the Southeastern Symposium on System Theory, University of Texas at Tyler, March 7-9, 2010, p. 9-14.
- J.M. Davis, I.A. Gravagne, R.J. Marks II, J.E. Miller, A.A. Ramos, Stability of switched linear systems on non-uniform time domains, IEEE Proceedings of the 42nd Meeting of the Southeastern Symposium on System Theory, University of Texas at Tyler, March 7-9, 2010, p. 127-132.
- J.M. Davis, I.A. Gravagne, R.J. Marks II, A.A. Ramos, Algebraic and dynamic Lyapunov equations on time scales, IEEE Proceedings of the 42nd Meeting of the Southeastern Symposium on System Theory, University of Texas at Tyler, March 7-9, 2010, p. 329-334.
- J.M. Davis, I.A. Gravagne, and R.J. Marks II, Bilateral Laplace transforms on time scales: convergence, convolution, and the characterization of stationary stochastic time series, Circuits, Systems, and Signal Processing, 29 (2010), 1141-1165.
- J.M. Davis, I.A. Gravagne, and R.J. Marks II, Convergence of unilateral Laplace transforms on time scales, Circuits, Systems, and Signal Processing, 29 (2010), 971-997.
- I.A. Gravagne, J.M. Davis, J.J. DaCunha, A unified approach to high-gain adaptive controllers, Abstract and Applied Analysis 2009 (2009), 1-13. arXiv:0901.3873v1 [math.OC]
- J.M. Davis, I.A. Gravagne, B.J. Jackson, R.J. Marks II, Controllability, observability, realizability, and stability of dynamic linear systems, Electronic Journal of Differential Equations 2009 (2009), 1-32. arXiv:0901.3764 [math.OC]
- R.J. Marks II, I.A. Gravagne, J.M. Davis, A generalized Fourier transform and convolution on time scales, Journal of Mathematical Analysis and Applications 340 (2008), 901-919.
- J.M. Davis, I.A. Gravagne, B.J. Jackson, R.J. Marks II, A.A. Ramos, The Laplace transform on time scales revisited, Journal of Mathematical Analysis and Applications 332 (2007), 1291–1307.
- R.J. Marks II, I.A. Gravagne, J.M. Davis, and J.J. DaCunha, Nonregressivity in switched linear circuits and mechanical systems, Mathematical and Computer Modelling 43 (2006), 1383–1392.
- Q. Sheng, M. Fadag, J. Henderson, and J.M. Davis, An exploration of combined dynamic derivatives on time scales and their applications, Nonlinear Analysis 7 (2006), 395–413.
- I.A. Gravagne, J.M. Davis, R.J. Marks II, How deterministic must a real-time controller be?, Proceedings of 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2005), Alberta, Canada, Aug. 2005, 3856–3861.
- I.A. Gravagne, J.M. Davis, R.J. Marks II. Bandwidth reduction for controller area networks using adaptive sampling, Proceedings of 2004 IEEE International Conference on Robotics and Automation (ICRA 2004), New Orleans, LA, April 2004, 5250–5255.
See my CV for a complete list of publications.