Title :
A necessary and sufficient condition for the existence of a nonlinear observer with linearizable error dynamics
Author :
Krener, Arthur J. ; Xiao, MingQing
Author_Institution :
Dept. of Math., California Univ., Davis, CA, USA
Abstract :
We provide a necessary and sufficient condition for the existence of nonlinear observer with linearizable error dynamics. The result is applicable to any real analytic observable nonlinear system. The necessary and sufficient condition is the solvability of a first-order nonlinear partial differential equation (PDE). The solution yields a change of state coordinates which linearizes the error dynamics. Under very general conditions, the existence and uniqueness of the solution is proved. Siegel´s theorem is obtained as a corollary. The technique is constructive and yields a method for constructing approximate solutions
Keywords :
approximation theory; computability; errors; linearisation techniques; nonlinear differential equations; nonlinear dynamical systems; observers; partial differential equations; Siegel domains; Siegel´s theorem; analytic observable nonlinear system; approximate solutions; error dynamics linearization; first-order nonlinear partial differential equation; linearizable error dynamics; necessary condition; nonlinear observer existence; nonlinear systems; output injection; solution uniqueness; solvability; state coordinates; sufficient condition; Differential equations; Ear; Eigenvalues and eigenfunctions; Mathematics; Nonlinear dynamical systems; Nonlinear systems; Observers; State estimation; Sufficient conditions; Vectors;
Conference_Titel :
Decision and Control, 2001. Proceedings of the 40th IEEE Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
0-7803-7061-9
DOI :
10.1109/.2001.980722
