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

TL;DR

This paper develops preliminary stochastic control results for aperiodic sample-data linear systems, using Ito's lemma to relate system stability to eigenvalues' expectations, applicable even with large or infinite sampling intervals.

Contribution

It introduces a stochastic control framework for aperiodic sample-data systems, extending stability conditions to systems with arbitrarily large or infinite sampling intervals.

Findings

Eigenvalues' expectation determines system stability.

Stability conditions hold even with large or infinite sampling intervals.

Experimental results verify the theoretical predictions.

Abstract

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.