Transfer Matrices and Statistical Analysis of Sampled-data Systems with Continuous Periodic Processes

The paper considers the statistical analysis problem for closed-loop sampled-data control systems. Hereby, a periodic non-stationary continuous-time process is fed back by a digital controller under the assumption that the sampling period coincides with the period of the continuous-time process. The analysis is based on the investigation of the parametric transfer matrix (PTM) for the whole system. A closed formula for constructing the parametric transfer matrix of the closed-loop system W(s,t) is provided, and its properties as functions of the variable s are investigated. On basis of these stated properties of the PTM W(s,t), a constructive method for calculating the variance of the quasi-stationary output dy(t) = dy(t+T) is derived. In practical applications, the mean variance of the output for excitation by stationary random white noise is of interest. An appropriate formula for this system characteristic is provided. The application of the statistical analysis method is demonstrated by an example.