Title :
Zero and pole dynamics for a controlled Burgers´ equation
Author :
Byrnes, C.I. ; Gilliam, D.S. ; Shubov, V.I.
Author_Institution :
Dept. of Syst. Sci. & Math., Washington Univ., St. Louis, MO, USA
Abstract :
Our primary goal is to report on the results obtained in the author´s recent work (1994) for a closed loop boundary controlled Burgers´ system with dynamics in the state space of square integrable functions on a finite interval. For small initial data and disturbances in L2, we have shown that as the closed loop system gains lend to infinity, the trajectories of the closed loop system converge in L2 to the trajectories of the zero dynamics, i.e., the systems obtained by constraining the system output to zero. For slightly stronger assumptions on the external forcing term (disturbance) it can be shown that the trajectories converge in H1(0,1) and hence uniformly
Keywords :
closed loop systems; distributed parameter systems; dynamics; feedback; nonlinear systems; poles and zeros; state-space methods; closed loop boundary; closed loop system gains; controlled Burgers´ equation; distributed parameter system; dynamics; nonlinear systems; pole dynamics; square integrable functions; state space; trajectory convergence; zero dynamics; Actuators; Closed loop systems; Control systems; Equations; Feedback; Nonlinear control systems; Nonlinear systems; Open loop systems; Poles and zeros; State-space methods;
Conference_Titel :
Decision and Control, 1994., Proceedings of the 33rd IEEE Conference on
Conference_Location :
Lake Buena Vista, FL
Print_ISBN :
0-7803-1968-0
DOI :
10.1109/CDC.1994.410914
