Abstract/Details

## Stability and control analysis of stochastic bilinear systems

Wing, Philip Lewis.
University of South Florida ProQuest Dissertations Publishing,  1994. 9426089.

### Abstract (summary)

The dissertation investigates the stability of stochastic bilinear differential systems with feedback control. System coefficients vary with time. The feedback function is in a function space which includes functions which are quadratic in the $L\sp2$ norm, and those satisfying a Lipschitz condition in the $L\sp2$ norm. Sufficient conditions for stability, asymptotic stability, and boundedness are given.

The author extends the results from continuous variables to the discrete case. Optimal feedback control is then applied to discrete statistical time series with constant coefficients. The deterministic model is shown to be controllable; this controllability then yields stability. Conditions for finite cost of the infinite horizon stochastic model are given.

The author presents results of simulations of the deterministic and stochastic models, including the fit of computer-generated costs to costs of the theoretical models themselves. Estimators for several model parameters are provided for several distinct estimation situations.

### Indexing (details)

Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
Stability and control analysis of stochastic bilinear systems
Author
Wing, Philip Lewis
Number of pages
112
Degree date
1994
School code
0206
Source
DAI-B 55/05, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-209-07093-1
Rao, A. N. V.
University/institution
University of South Florida
University location
United States -- Florida
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9426089
ProQuest document ID
304128943