TY - JOUR

T1 - A formula for frequency responses of distributed systems with one spatial variable

AU - Jovanović, Mihailo R.

AU - Bamieh, Bassam

PY - 2006/1/1

Y1 - 2006/1/1

N2 - We develop a method for the exact determination of frequency responses for a class of infinite dimensional systems. In particular, we consider distributed systems in which a spatial independent variable belongs to a finite interval, and in which the inputs and outputs are spatially distributed over the same interval. We show that an explicit formula for the Hilbert-Schmidt norm of the operator-valued frequency response can be obtained whenever the underlying operators are represented by a forced two point boundary value state-space realizations (TPBVSR). This formula involves finite dimensional computations with matrices whose dimension is at most four times larger than the order of the underlying differential operator. Two examples are provided to illustrate the procedure.

AB - We develop a method for the exact determination of frequency responses for a class of infinite dimensional systems. In particular, we consider distributed systems in which a spatial independent variable belongs to a finite interval, and in which the inputs and outputs are spatially distributed over the same interval. We show that an explicit formula for the Hilbert-Schmidt norm of the operator-valued frequency response can be obtained whenever the underlying operators are represented by a forced two point boundary value state-space realizations (TPBVSR). This formula involves finite dimensional computations with matrices whose dimension is at most four times larger than the order of the underlying differential operator. Two examples are provided to illustrate the procedure.

KW - Frequency responses

KW - Infinite-dimensional systems

KW - Two point boundary value state-space realizations

UR - http://www.scopus.com/inward/record.url?scp=28444453271&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28444453271&partnerID=8YFLogxK

U2 - 10.1016/j.sysconle.2005.04.014

DO - 10.1016/j.sysconle.2005.04.014

M3 - Article

AN - SCOPUS:28444453271

VL - 55

SP - 27

EP - 37

JO - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

IS - 1

ER -