cascade systems; delay equations; nonlinear control
Abstract :
[en] In this paper the effect of bounded input perturbation on the stability of nonlinear globally asymptotically stable delay differential equations is analyzed. We investigate under which conditions global stability in preserved and if not, whether semi-global stabilization is possible by controlling the size or shape of the perturbation. This results in a general framework, in which the stabilization of partial linear cascade systems using partial state feedback can be treated systematically.
Disciplines :
Electrical & electronics engineering
Author, co-author :
Michiels, Wim; Katholieke Universiteit Leuven - KUL
Sepulchre, Rodolphe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation
Roose, Dirk; Katholieke Universiteit Leuven - KUL
Language :
English
Title :
Stability of perturbed functional differential equations and stabilization of nonlinear cascades
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Byrnes C., Isidori A. (1991) Asymptotic stability of minimum phase nonlinear systems. IEEE Trans. Automat. Control 36:1122-1137.
Hale J., Verduyn Lunel S.M. (1993) Introduction to functional differential equations. Appl. Math. Sci. , Springer-Verlag, New York; 99.
Isidori A. (1995) Nonlinear control systems, 3rd ed. Comm. Control Engrg. Ser., Springer-Verlag, Berlin; .
Kolmanovskii V., Myshkis A. (1999) Introduction to the theory and application of functional differential equations. Math. Appl. , Kluwer Academic Publishers, Dordrecht, The Netherlands; 463.
Kolmanovskii V., Nosov V. (1986) Stability of functional differential equations. Math. Sci. Engrg. , Academic Press, San Diego, CA; 180.
Lin Z., Saberi A. (1993) Semi-global stabilization of partially linear composite systems via feedback of the state of the linear part. Systems Control Lett. 20:199-207.
Middleton R. (1991) Trade-offs in linear control system design. Automatica J. IFAC 27:281-292.
Sepulchre R., Janković M., Kokotović P. (1997) Constructive nonlinear control. Comm. Control Engrg., Springer-Verlag, Berlin; .
Sontag E. (1995) On the input-to-state stability properties. European J. Control 1:24-36.
Sussmann H., Kokotovic P. (1991) The peaking phenomenon and the global stabilization of nonlinear systems. IEEE Trans. Automat. Control 36:424-440.
Teel A. (1996) A nonlinear small gain theorem for the analysis of control systems with saturation. IEEE Trans. Automat. Control 41:1256-1270.
Teel A., Praly L. (1995) Tools for semiglobal stabilization by partial state and output feedback. SIAM J. Control Optim. 33:1443-1488.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
