Robust Stability Bound on Linear Time-Varying Uncertainties for Linear Digital Control Systems under Finite Wordlength Effects

Abstract

An approach is introduced to analyze the robust stability of linear digital control systems under both finite wordlength effects and linear time-varying parameter perturbations. Digital controllers are realized with floating-point arithmetic. The 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 parameter perturbations, feedback gain quantization error and computational roundoff errors. This bound provides a quantitative measure for control engineers to design an actual closed-loop digital control system with robustness. An example is given to illustrate the application of the proposed robust stability criterion.