Stochastic frequency characteristics (Q2753219)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Stochastic frequency characteristics |
scientific article; zbMATH DE number 1667496
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stochastic frequency characteristics |
scientific article; zbMATH DE number 1667496 |
Statements
29 October 2001
0 references
coercivity
0 references
frequency characteristics
0 references
indefinite stochastic linear-quadratic problem
0 references
control
0 references
stochastic Riccati equation
0 references
bilinear form
0 references
Stochastic frequency characteristics (English)
0 references
The paper is concerned with stochastic linear-quadratic (LQ) problems in infinite time horizon with control-dependent diffusions and indefinite cost weighting matrices. A new frequency characteristic for the indefinite stochastic LQ problem is obtained. This characteristic is a complex matrix that can be calculated directly from the given parameters of the LQ problem. The equivalence of the following statements is established: 1) the LQ problem is solvable and has a unique optimal control; 2) the stochastic Riccati equation has a unique solution such that the induced feedback control is stabilizing; 3) the associated optimization problem of the bilinear form is coercive; and 4) the frequency characteristic matrix is uniformly positive definite.
0 references
