Stochastic analysis of dead-time systems using a hybrid spectral method

Abstract

Control systems often operate in the presence of dead-time. However, in most works, these dead-time systems are studied in a deterministic manner, which have low precision and reliability. Many natural systems often suffer stochastic noise that causes fluctuations in their behavior, making their responses deviate from nominal models. Therefore, it is important to investigate such statistical characteristic of states (mean, variance, etc.) for those stochastic systems. This problem is often called statistical analysis of a system. A hybrid spectral method represents a powerful numerical tool for statistical analysis of stochastic linear system. Thus, a hybrid spectral technique is proposed for statistical analysis of the time delay system under affections of random parameters and inputs. Numerical examples are considered to demonstrate the validity of the proposed method. Comparison with the traditional Monte-Carlo and the polynomial chaos methods is made to demonstrate the computationally lessdemanding feature of the proposed method.