Preliminary result on stochastic system control theory for aperiod sample-data systems
Provides a theoretical foundation for stability analysis of aperiodic sample-data systems, which is relevant for control engineers dealing with irregular sampling.
The paper develops a stochastic control theory for time-varying linear systems and applies it to aperiodic sample-data systems, showing that stability depends on the expectation of the system matrix eigenvalues and sample interval, allowing arbitrarily large aperiodic intervals.
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.