Stability and control analysis of stochastic bilinear systems

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.