Article

Giesl, Peter (2019) Converse theorem on a global contraction metric for a periodic orbit. Discrete and Continuous Dynamical Systems - Series A. ISSN 1078-0947 (Accepted)

Giesl, Peter (2019) Construction of Finsler-Lyapunov functions with meshless collocation. ZAMM. ISSN 0044-2267

Giesl, Peter and Wendland, Holger (2018) Kernel-based discretisation for solving matrix-valued PDEs. SIAM Journal on Numerical Analysis, 56 (6). pp. 3386-3406. ISSN 0036-1429

Bjoernsson, Hjortur, Hafstein, Sigurdur, Giesl, Peter, Scalas, Enrico and Gudmundsson, Skuli (2018) Computation of the stochastic basin Of attraction by rigorous construction of a lyapunov function. Discrete and Continuous Dynamical Systems - Series B. ISSN 1531-3492 (Accepted)

Giesl, Peter and Mohammed, Najla (2018) Verification estimates for the construction of Lyapunov functions using meshfree collocation. Discrete & Continuous Dynamical Systems Ser. B. ISSN 1531-3492 (Accepted)

Giesl, Peter and Wendland, Holger (2018) Construction of a contraction metric by meshless collocation. Discrete and Continuous Dynamical Systems - Series B. ISSN 1531-3492 (Accepted)

Giesl, Peter and McMichen, James (2018) Determination of the area of exponential attraction in one-dimensional finite-time systems using meshless collocation. Discrete and Continuous Dynamical Systems - Series B. ISSN 1531-3492

Hafstein, Sigurdur, Gudmundsson, Skuli, Giesl, Peter and Scalas, Enrico (2018) Lyapunov function computation for autonomous linear stochastic differential equations using sum-of-squares programming. Discrete and Continuous Dynamical Systems - Series B, 23 (2). pp. 939-956. ISSN 1531-3492

Giesl, Peter and McMichen, James (2017) Determination of the basin of attraction of a periodic orbit in two dimensions using meshless collocation. Journal of Computational Dynamics, 3 (2). pp. 191-210. ISSN 2158-2491

Giesl, Peter and Hafstein, Sigurdur (2015) Computation and verification of Lyapunov functions. SIAM Journal on Applied Dynamical Systems, 14 (4). pp. 1663-1698. ISSN 1536-0040

Giesl, Peter and Mohammed, Najla (2015) Grid refinement in the construction of Lyapunov functions using radial basis functions. Discrete and Continuous Dynamical Systems - Series B, 20 (8). pp. 2453-2476. ISSN 1531-3492

Giesl, Peter and Hafstein, Sigurdur (2015) Review on computational methods for Lyapunov functions. Discrete and Continuous Dynamical Systems - Series B, 20 (8). pp. 2291-2331. ISSN 1531-3492

Giesl, Peter and Hafstein, Sigurdur (2015) Review on computational methods for Lyapunov functions. Discrete and Continuous Dynamical Systems - Series B, 20 (8). pp. 2291-2331. ISSN 1531-3492

Björnsson, Jóhann, Giesl, Peter, Hafstein, Sigurdur F and Kellett, Christopher M (2015) Computation of Lyapunov functions for systems with multiple attractors. Discrete and Continuous Dynamical Systems - Series A, 35 (9). pp. 4019-4039. ISSN 1078-0947

Giesl, Peter (2015) Converse theorems on contraction metrics for an equilibrium. Journal of Mathematical Analysis and Applications, 424 (2). pp. 1380-1403. ISSN 0022-247X

Giesl, Peter (2015) Converse theorems on contraction metrics for an equilibrium. Journal of Mathematical Analysis and Applications, 424 (2). pp. 1380-1403. ISSN 0022-247X

Kellett, Christopher M, Hafstein, Sigurdur F, Giesl, Peter and Björnsson, Jóhann (2015) Computation of Lyapunov functions for systems with multiple local attractors. Discrete and Continuous Dynamical Systems, 35 (9). pp. 4019-4039. ISSN 1078-0947

Giesl, Peter A and Hafstein, Sigurdur F (2014) Revised CPA method to compute Lyapunov functions for nonlinear systems. Journal of Mathematical Analysis and Applications, 410 (1). pp. 292-306. ISSN 0022-247X

Giesl, Peter and Hafstein, Sigurdur (2014) Computation of Lyapunov functions for nonlinear discrete systems by linear programming. Journal of Difference Equations and Applications, 20 (4). pp. 610-640. ISSN 1023-6198

Björnsson, Jóhann, Giesl, Peter and Hafstein, Sigurður (2014) Algorithmic verification of approximations to complete Lyapunov functions. Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS), Groningen, The Netherlands, 0180. pp. 1181-1188.

Giesl, Peter and Hafstein, Sigurður (2014) Implementation of a fan-like triangulation for the CPA method to compute Lyapunov functions. Proceedings of the 2014 American Control Conference, Portland (OR), USA, 2014, 0202. pp. 2989-2994.

Giesl, Peter and Hafstein, Sigurdur (2013) Construction of a CPA contraction metric for periodic orbits using semidefinite optimization. Nonlinear Analysis: Theory, Methods & Applications, 86. pp. 114-134. ISSN 0362-546X

Giesl, Peter (2012) Construction of a finite-time Lyapunov function by meshless collocation. Discrete and Continuous Dynamical Systems - Series B, 17 (7). pp. 2387-2412. ISSN 1531-3492

Giesl, Peter and Hafstein, Sigurdur (2012) Existence of piecewise linear Lyapunov functions in arbitrary dimensions. Discrete and Continuous Dynamical Systems - Series A, 32 (10). pp. 3539-3565. ISSN 1078-0947

Giesl, Peter and Rasmussen, Martin (2012) Areas of attraction for nonautonomous differential equations on finite time intervals. Journal of Mathematical Analysis and Applications, 390 (1). pp. 27-46. ISSN 0022-247X

Giesl, Peter and Hafstein, Sigurdur (2012) Construction of Lyapunov functions for nonlinear planar systems by linear programming. Journal of Mathematical Analysis and Applications, 388 (1). pp. 463-479. ISSN 0022-247X

Giesl, Peter and Wendland, Holger (2012) Numerical determination of the basin of attraction for asymptotically autonomous dynamical systems. Nonlinear Analysis: Theory, Methods and Applications, 75 (5). pp. 2823-2840. ISSN 0362-546X

Giesl, Peter and Wendland, Holger (2011) Numerical determination of the basin of attraction for exponentially asymptotically autonomous dynamical systems. Nonlinear Analysis: Theory, Methods and Applications, 74 (10). pp. 3191-3203. ISSN 0362-546X

Giesl, Peter and Rasmussen, Martin (2011) A note on amost periodic variational equations. Communications on Pure and Applied Analysis, 10 (3). pp. 983-994. ISSN 1534-0392

Giesl, Peter and Hafstein, Sigurdur (2010) Existence of piecewise affine Lyapunov functions in two dimensions. Journal of Mathematical Analysis and Applications, 371 (1). pp. 233-248. ISSN 0022-247X

Giesl, Peter and Wendland, Holger (2009) Approximating the basin of attraction of time-periodic ODEs by meshless collocation. Discrete and Continuous Dynamical Systems - Series A, 25 (4). pp. 1249-1274. ISSN 1078-0947

Giesl, Peter (2009) On the determination of the basin of attraction of periodic orbits in three- and higher-dimensional systems. Journal of Mathematical Analysis and Applications, 354 (2). pp. 606-618. ISSN 0022-247X

Giesl, Peter and Rasmussen, Martin (2008) Borg's criterion for almost periodic differential equations. Nonlinear Analysis: Theory, Methods and Applications, 69 (11). pp. 3722-3733. ISSN 0362-546X

Giesl, Peter (2008) Construction of a local and global Lyapunov function for discrete dynamical systems using radial basis functions. Journal of Approximation Theory, 153 (2). pp. 184-211. ISSN 0021-9045

Giesl, Peter (2008) Construction of a local and global Lyapunov function using radial basis functions. IMA Journal of Applied Mathematics, 73 (5). pp. 782-802. ISSN 0272-4960

Giesl, Peter (2007) On the determination of the basin of attraction of a periodic orbit in two-dimensional systems. Journal of Mathematical Analysis and Applications, 335 (1). pp. 461-479. ISSN 0022-247X

Giesl, Peter and Wendland, Holger (2007) Meshless Collocation: Error estimates with application to dynamical systems. SIAM Journal on Numerical Analysis, 45 (4). pp. 1723-1741. ISSN 1095-7170

Giesl, Peter (2007) Necessary condition for the basin of attraction of a periodic orbit in non-smooth periodic systems. Discrete and Continuous Dynamical Systems - Series A, 18 (2-3). pp. 355-373. ISSN 1078-0947

Giesl, Peter and Wagner, Heiko (2007) Lyapunov functions and the basin of attraction for a single-joint muscle-skeletal model. Journal of Mathematical Biology, 54 (4). pp. 453-464. ISSN 0303-6812

Giesl, Peter (2007) Construction of a global Lyapunov function using radial basis functions with a single operator. Discrete and Continuous Dynamical Systems - Series B, 7 (1). pp. 101-124. ISSN 1531-3492

Wagner, Heiko, Giesl, Peter and Blickhan, Reinhard (2007) Musculoskeletal Stabilization of the Elbow - Complex or Real. Journal of Mechanics in Medicine and Biology, 7 (3). pp. 275-296. ISSN 0219-5194

Giesl, Peter (2007) On the determination of the basin of attraction of discrete dynamical systems. Journal of Difference Equations and Applications, 13 (6). pp. 523-546. ISSN 1023-6198

Giesl, P (2005) The basin of attraction of periodic orbits in nonsmooth differential equations. Zeitschrift fur Angwandte Mathematik und Mechanik, 85 (2). pp. 89-104. ISSN 0044-2267

Giesl, Peter, Meisel, Dorothea, Scheurle, Jürgen and Wagner, Heiko (2004) Stability analysis of the elbow with a load. Journal of Theoretical Biology, 228 (1). pp. 115-125. ISSN 0022-5193

Giesl, Peter (2004) Necessary conditions for a limit cycle and its basin of attraction. Nonlinear Analysis: Theory, Methods and Applications, 56 (5). pp. 643-677. ISSN 0362-546X

Giesl, Peter (2004) On the basin of attraction of limit cycles in periodic differential equations. Zeitschrift fur Analysis und ihre Anwendungen, 23 (3). pp. 547-576. ISSN 0232-2064

Giesl, P (2003) Unbounded basins of attraction of limit cycles. Acta Mathematica Universitatis Comenianae, 72 (1). pp. 81-110. ISSN 0862-9544

Book Section

Björnsson, J, Giesl, P, Hafstein, S, Kellett, C M and Li, H (2014) Computation of continuous and piecewise affine Lyapunov functions by numerical approximations of the Massera construction. In: 2014 IEEE 53rd Annual Conference on Decision and Control (CDC). IEEE, pp. 5506-5511. ISBN 9781479977468

Giesl, Peter and Hafstein, Sigurdur (2013) Local Lyapunov functions for periodic and finite-time ODEs. In: Johann, Andreas, Kruse, Hans-Peter, Rupp, Florian and Schmitz, Stephan (eds.) Recent Trends in Dynamical Systems. Springer Proceedings in Mathematics & Statistics . Springer, Basel, pp. 125-152. ISBN 9783034804509

Giesl, Peter (2011) Towards calculating the basin of attraction of non-smooth dynamical systems using radial basis functions. In: Georgoulis, E, Iske, A and Levesley, J (eds.) Approximation Algorithms for Complex Systems. Springer Proceedings in Mathematics, 3 . Springer-Verlag, pp. 205-225. ISBN 9783642168758

Giesl, Peter, Ernst, Michael and Wagner, Heiko (2010) Einzugsbereiche eines menschlichen Armmodells: Eine Analyse basierend auf Lyapunovfunktionen. In: Ertelt, T (ed.) Beiträge zur Bewegungswissenschaft Band 1. Verlag Dr. Kovac, Hamburg, pp. 97-134. ISBN 9783830046509

Giesl, Peter and Wagner, H (2009) Mathematical Stability Analysis in Biomechanical Applications. In: Wilson, LB (ed.) Mathematical Biology Research Trends. Nova Science Publishers. ISBN 978-1-61668-394-8

Mombaur, Katja, Giesl, Peter and Wagner, Heiko (2008) Stability Optimization of Juggling. In: Bock, HG, Kostina, E, Hoang, XP and Rannacher, R (eds.) Modeling, Simulation and Optimization of Complex Processes. Springer Berlin Heidelberg, pp. 419-432. ISBN 978-3-540-79408-0

Giesl, Peter (2007) Stepwise calculation of the basin of attraction in dynamical systems using radial basis functions. In: Iske, A and Levesly, J (eds.) Algorithms for approximation: proceedings of the 5th international conference. Algorithms for Approximation . Springer -Verlag, Berlin, Germany, pp. 113-122. ISBN 9783540332831

Giesl, P and Wagner, H (2006) On the Determination of the Basin of Attraction for Stationary and Periodic Movements. In: Diehl, M and Mombaur, K (eds.) Fast Motions in Biomechanics and Robotics. Springer Berlin / Heidelberg. ISBN 978-3-540-36118-3

Wagner, H and Giesl, P (2006) Self-stability in Biological Systems - Studies based on Biomechanical Models. In: Diehl, M and Mombaur, K (eds.) Fast Motions in Biomechanics and Robotics. Springer Berlin / Heidelberg. ISBN 978-3-540-36118-3

Giesl, Peter (2005) Stimmung und Kettenbrüche. In: Stahnke, M (ed.) Mikrotöne und mehr: Auf György Ligetis Hamburger Pfaden. von Bockel Verlag, Hamburg, Germany. ISBN 393269662X

Conference or Workshop Item

Giesl, Peter and Wendland, Holger (2009) Approximating the basin of attraction of time-periodic ODEs by meshless collocation of a Cauchy problem. In: Discrete Contin. Dyn. Syst. Supplement.

Giesl, Peter (2009) The flow of harmony as a dynamical system. In: 1st International Conference on Mathematics and Computation in Music, 18-20 May, 2007, Berlin, Germany.

Wagner, H and Giesl, P (2006) Self-stability in biological systems - Studies based on biomechanical models. In: Lecture Notes in Control and Information Sciences.

Giesl, Peter (2003) The optimal elbow angle for acrobatics - stability analysis of the elbow with a load. In: Proceedings in applied mathematics and mechanics.

Conference Proceedings

Argaez, Carlos, Hafstein, Sigurdur and Giesl, Peter (2017) Wendland functions a C++ code to compute them. SIMULTECH 2017, Madrid, Spain, 26/07/17 - 28/07/17. Published in: Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, 2017, Madrid, Spain. 323-330. SCITEPRESS, Madrid, Spain. ISBN 9789897582653

Argáez, Carlos, Giesl, Peter and Hafstein, Sigurdur (2017) Analysing dynamical systems towards computing complete Lyapunov functions. SIMULTECH 2017, Madrid, Spain, 26/07/17 - 28/07/17. Published in: Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, 2017, Madrid, Spain. 134-144. Madrid, Spain. ISBN 9789897582653

Book

Giesl, Peter (2007) Construction of global Lyapunov functions using radial basis functions. Lecture Notes in Mathematics, 1904 (190). Springer, Berlin and Heidelberg. ISBN 9783540699071