Transfer Matrices and Advanced Statistical Analysis of Digital Controlled Continuous-Time Periodic Processes with Delay

The paper investigates the response of a closed-loop sampled-data system S with an finite dimensional linear continuous periodic (FDLCP) process and pure delay to a stationary stochastic input. Since the variance of the quasi-stationary output of the system S is a periodic function of the time, an advanced form of statistical analysis is required. The paper introduces the advanced statistical analysis problem, and its solution is derived on basis of the parametric transfer matrix (PTM) concept. Moreover, a characteristic polynomial is defined, which gives necessary and sufficient conditions for the asymptotic stability of the system S. An example demonstrates the advanced statistical analysis procedure.