Title :
Exact computation of traces and H2 norms for a class of infinite dimensional problems
Author :
Bamieh, Bassam ; Dahleh, Mohammed
Author_Institution :
Dept. of Mech. & Environ. Eng., California Univ., Santa Barbara, CA, USA
Abstract :
We derive a formula for the trace of a class of differential operators defined by forced two point boundary value problems. The formula involves finite dimensional computations with matrices whose dimension is no larger than the order of the differential operator. We thus achieve an exact reduction of an infinite dimensional problem to a finite dimensional one. We relate this trace calculation to computation of the H2 norm for certain infinite dimensional systems. An example from hydrodynamic stability is included to illustrate the method
Keywords :
boundary-value problems; matrix algebra; multidimensional systems; state-space methods; H2 norms; differential operators; finite dimensional computations; finite dimensional problems; forced two point boundary value problems; infinite dimensional problems; traces; Boundary conditions; Boundary value problems; Control theory; Differential equations; Eigenvalues and eigenfunctions; Engineering profession; Hydrodynamics; Kernel; Stability; State-space methods;
Conference_Titel :
American Control Conference, 2000. Proceedings of the 2000
Conference_Location :
Chicago, IL
Print_ISBN :
0-7803-5519-9
DOI :
10.1109/ACC.2000.878587
