It can be shown that kLP k1 > 1 for h > 0:115. Hence the test fails to detect the stability of this uncertain delay system. IV. CONCLUSIONS All results presented in the previous section can be generalized to synthesis of uncertain delay systems. In fact, we can also include other types of uncertainties and disturbances easily using the general linear… (More)
Neutral stochastic differential delay equations (NSDDEs) have recently been studied intensively (Given that many systems are often subject to component failures or repairs, changing subsystem interconnections and abrupt environmental disturbances etc., the structure and parameters of underlying NSDDEs may change abruptly.
The stochastic diierence equations with Volterra type linear and non-linear main term are considered in the paper. Conditions on a.s. bound-edness of the solutions, asymptotic stability, exponential stability, and stability with a speed which is diiers from the exponential, are obtained. A numerous examples are presented.
The general method of Lyapunov functionals construction for stability investigation of stochastic hereditary systems which was proposed and developed before is considered. Some features of this method for difference systems which allow one to use the method more effectively are discussed.