Hyperstability and average hyperstability conditions for a broad class of gaussian stochastic systems

The author investigates the hyperstability problem for a broad class of single-control stochastic systems which may be considered as disturbed models of given deterministic systems. The stochasticity comes from the control, which is disturbed by an additive Gaussian noise with its own gain. Hyperstability conditions are given when the noise has a time-independent variance. When this variance depends explicitly upon the time, we define the time-average hyperstability, and conditions for average hyperstability are given. Similar problems are solved for multicontrol Gaussian systems. Illustrative examples show how one can derive from these results a broad class of absolute stability conditions.