Stabilizability and Controllability of Spatially Invariant P.D.E. Systems

Author

Curtain, Ruth F.

Author_Institution

Bernoulli Inst. for Math. & Comput. Sci., Univ. of Groningen, Groningen, Netherlands

Volume

60

Issue

2

fYear

2015

fDate

Feb. 2015

Firstpage

383

Lastpage

392

Abstract

In this paper, we derive new readily testable criteria for exponential stabilizability, approximate controllability, and exact controllability for multiplicative systems arising from linear partial differential equations on an infinite domain. These multiplicative systems have an unbounded semigroup generator, but bounded input and output operators. The theoretical results are illustrated by several examples. In particular, explicit, easily verifiable conditions for exponential stabilizability, approximate and exact controllability are given for second-order P.D.E. systems. Dual results for exponential detectability, approximate and exact observability are also included.

Keywords

approximation theory; asymptotic stability; controllability; group theory; linear differential equations; matrix multiplication; observability; partial differential equations; approximate controllability; approximate observability; bounded input operators; bounded output operators; exact controllability; exact observability; exponential detectability; exponential stabilizability; infinite domain; linear partial-differential equations; multiplicative systems; spatially invariant PDE systems; unbounded semigroup generator; verifiable conditions; Controllability; Generators; Hilbert space; Observability; Riccati equations; Zinc; Controllability; distributed parameter systems; spatially invariant systems; stabilizability;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2014.2348212

Filename

6879303