Exact controllability theorems for linear parabolic equations in one space dimension
β Scribed by H. O. Fattorini; D. L. Russell
- Publisher
- Springer
- Year
- 1971
- Tongue
- English
- Weight
- 798 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0003-9527
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
A be an n X n complex matrix with inertia In(A) = (r(A), a(A), s(A)), and let H be an n x n hermitian matrix with inertia In(H) = (r(H), 6(H), 6(H)). Let K b e an n X n positive semidefinite matrix such that K = AH + HA\*. Suppose that 1 is the dimension of the controllability space of the pair (A,
0010-13640/81/00344029S2.30 'I$ need not even be defined for all arguments, since u' and u" will stay small for sufficiently small norms off, g. 2Solutions of the one-dimensional problem (4a, b) can also be viewed as special solutions u(x.r) of the n-dimensional equation u,, = c(u,,)Au which happen
A criterion of exact controllability using the resolvent of the state space operator is given for linear control system in Hilbert space. Only surjectivity of the semigroup operators is assumed. This condition is necessary for exact controllability, so the criterion is quite general. Relations betwe