Publication Cover
Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 9
104
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Exponential stabilizability of nonlinear control systems in Banach spaces

Pages 2017-2028 | Received 21 Oct 2014, Accepted 14 Aug 2015, Published online: 11 Sep 2015

References

  • Anderson BD, Ilchmann A, Wirth F. Stabilizability of linear time-varying systems. Syst. Control Lett. 2013;62:747–755.
  • Amato F, Celentano G, Garofalo F. New sufficient conditions for the stability of slowly varying linear systems. IEEE Trans. Autom. Control. 1993;38:1409–1411.
  • Benabdallah A, Hammami MA. On the output feedback stability of nonlinear uncertain control systems. Int. J. Control. 2001;74:547–551.
  • Chukwu EN. Stability and time-optimal control of hereditary systems. New York (NY): Academic Press; 1992.
  • Feliachi A, Thowsen A. Memoryless stabilization of linear delay-differential systems. IEEE Trans. Autom. Control. 1981;586–587.
  • Medina R. Stabilization for nonlinear systems of difference equations. Int. J. Robust Nonlinear Control. 2010;20:1156–1165.
  • Wang J, Feckan M, Zhou Y. Relaxed controls for nonlinear fractional impulsive evolution equations. J. Optim. Theory Appl. 2013;156:13–32.
  • Wang J, Xiang X, Wei W. Stability analysis and periodic optimal control problems for impulsive periodic system. Math. Commun. 2011;16:235–250.
  • Sontag ED, Lin Y. Stabilization with respect to noncompact sets: Lyapunov characterizations and effect of bounded inputs. In: Proceedings of Nonlinear Control Systems Design Symposium, Bordeaux, France, 1992 Jun. p. 9–14.
  • Tsinias J. Existence of control Lyapunov functions and its applications to state feedback stabilizability of nonlinear systems. SIAM J. Control Optim. 1991;29:457–473.
  • Hale JK. Theory of functional differential equations. New York (NY): Springer-Verlag; 1977.
  • Khalil KK. Nonlinear systems. Englewood Cliffs (NJ): Prentice-Hall; 2002.
  • Kobayashi T. Feedback stabilization of parabolic distributed parameter systems by discrete-time input--output data. SIAM J. Control Optim. 1989;22:509–522.
  • Smirnov GB. Weak asymptotic stability of differential inclusions. Avtomat. i Telemekh. 1990;7:57–64.
  • Gil’ MI, Medina R. The freezing method for linear difference equations. J. Differ. Equ. Appl. 2001;8:485–494.
  • Ikeda M, Maeda H, Kodama S. Stabilization of linear systems. SIAM J. Control Optim. 1972;10:716–729.
  • Ikeda M, Maeda H, Kodama S. Estimation and feedback in linear time-varying systems: a deterministic theory. SIAM. J. Control Optim. 1975;13:304–326.
  • Jetto L, Orsini V. Relaxed conditions for the exponential stability of a class of linear time-varying systems. IEEE Trans. Autom. Control. 2009;54:1581–1585.
  • Hinrichsen D, Ilchmann A, Pritchard AJ. Robustness of stability of time-varying linear systems. J. Differ. Equ. 1989;82:219–250.
  • Kreisselmeir G. Adaptive control of a class of slowly time varying plants. Syst. Control Lett. 1986;8:97–103.
  • Rosenbrock HH. The stability of linear time-dependent control systems. Int. J. Elect. Control. 1961;15:73–80.
  • Bylov BF, Grobman BM, Nemickii VV, Vinograd RE. The theory of Lyapunov exponents. Moscow: Nauka; 1966.
  • Gil’ MI. Norm estimations for operator-valued functions and applications. New York (NY): Marcel Dekker; 1995.
  • Gel’fand IM, Shilov GE. Some questions on differential equations. Moscow: Nauka; 1958.
  • Daleckii YuL, Krein MG. Stability of solutions of differential equations in Banach spaces. Providence (RI): American Mathematical Society; 1971.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.