Robust stability measure for discrete‐time linear regulators with computational delays under finite wordlength effects and time‐varying parameter perturbations

Abstract

A non-Lyapunov approach is introduced to analyze the robust stability of discrete-time linear regulators with computational delays under both finite wordlength effects and linear time-varying parameter perturbations. A robust stability criterion (sufficient condition) presented in this paper can be used to obtain the stability bound on a linear time-varying uncertainty matrix due to the combination of linear timevarying parameter perturbations and computational roundoff errors. This bound provides a quantitative measure concerning robustness for control engineers to design actual discrete-time linear regulators with computational delays. An example is given to illustrate the application of the proposed robust stability criterion.