Contractive systems with inputs

Lecture Notes in Control and Information Sciences

Volumn 398, Issue , 2010, Pages 217-228

  Sontag, Eduardo D ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BASIC RESULTS; CONTRACTION THEORY; EXTERNAL INPUT; FORCING FUNCTION; INCREMENTAL STABILITY; LIMIT CYCLE; NON-EUCLIDEAN;

STABILITY;

SIGNAL PROCESSING;

EID: 77950208138     PISSN: 01708643     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-93918-4_20     Document Type: Article

References (21)

1. Angeli, D., Sontag, E.D.: Forward completeness, unboundedness observability, and their Lyapunov characterizations. Systems and Control Letters 38, 209-217 (1999).
2. Bauer, F.L., Stoer, J., Witzgall, C.: Absolute and monotonic norms. Numerische Mathematik 3, 257-264 (1961).
3. Dahlquist, G.: Stability and error bounds in the numerical integration of ordinary differential equations. Trans. Royal Inst. Technol., Stockholm (1959).
4. Demidovich, B.P.: Dissipativity of a nonlinear system of differential equations. Vestnik Moscow State University, Ser. Mat. Mekh. 6, 19-27 (1961) in Russian).
5. Desoer, C.A., Vidyasagar, M.: Feedback Synthesis: Input-Output Properties. SIAM, Philadelphia (2009).
6. Jouffroy, J., Slotine, J.J.E.:Methodological remarks on contraction theory. In: Proc. 42nd Conf. Decision and Control, pp. 2537-2543. IEEE Press, Los Alamitos (2004).
7. Lohmiller,W., Slotine, J.J.E.: Nonlinear process control using contraction theory. AIChe Journal 46, 588-596 (2000).
8. Lozinskii, S.M.: Error estimate for numerical integration of ordinary differential equations, I. Izv. Vtssh. Uchebn. Zaved. Mat. 5, 222 (1959).
9. Michel, A.N., Liu, D., Hou, L.: Stability of Dynamical Systems: Continuous, Discontinuous, and Discrete Systems. Springer, New York (2007).
10. Pavlov, A., Pogromvsky, A., van de Wouv, N., Nijmeijer, H.: Convergent dynamics, a tribute to Boris Pavlovich Demidovich. Systems & Control Letters 52, 257-261 (2004).
11. Pavlov, A., van de Wouw, N., Nijmeijer, H.: Uniform Output Regulation of Nonlinear Systems: A Convergent Dynamics Approach. Springer, Berlin (2005).
12. Russo, G., di Bernardo, M.: Contraction theory and the master stability function: linking two approaches to study synchronization in complex networks. IEEE Transactions on Circuit and Systems II 56, 177-181 (2009).
13. Russo, G., di Bernardo, M., Sontag, E.D.: Global entrainment of transcriptional systems to periodic inputs (submitted) preprint, 2009), http://arxiv.org/abs/0907.0017).
14. Söderlind, G.: The logarithmic norm: history and modern theory. BIT Numerical Mathematics 46, 631-652 (2006).
15. Sontag, E.D.: Mathematical Control Theory. In: Deterministic Finite-Dimensional Systems. Springer, New York (1998).
16. Sontag, E.D.: An observation regarding systems which converge to steady states for all constant inputs, yet become chaotic with periodic inputs. Technical report, arxiv 0906.2166 (2009).
17. Strom, T.: On logarithmic norms. SIAM J. Numer. Anal. 12, 741-753 (1975).
18. Vidyasagar, M.: Nonlinear Systems Analysis, 2nd edn. Pretice-Hall, Englewood Cliffs (1993).
19. Wang, W., Slotine, J.J.E.: On partial contraction analysis for coupled nonlinear oscillators. Biological Cybernetics 92, 38-53 (2005).
20. Yoshizawa, T.: Stability Theory by Liapunov's Second Method. The Mathematical Society of Japan, Tokyo (1966).
21. Yoshizawa, T.: Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions. Springer, New York (1975).