Title :
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
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;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2014.2348212
