Preliminary result on stochastic system control theory for aperiod sample-data systems

In this paper, we obtain some preliminary results on stochastic control theory for time-varying linear systems both continuous and discrete, and further apply to aperiod sample-data linear systems. The Ito's lemma is utilized in this proposed theory, and deduced that the stability of a linear time-varying system is determined by the eigenvalues expectation of system matrix, which coincidences with the stable conditions for time-invariant system, i.e. Hurwitz for continuous systems or inside the unit circle for discrete systems. The control method for aperiod time-invariant sample-data system is also derived. It is shown that the stable condition is determined by the expectation of the sample-interval but the up-bound and the aperiod interval can be arbitrarily large even infinity. To verify the efficiency of our theory, serval experiments are demonstrated in the final of the paper.