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

Robust stability analysis for discrete-time LQG system under finite wordlength effects, noise uncertainties and time-varying structured parameter perturbations

“…(11), (12), (14) and (15) Therefore, according to the robust stability condition (31), we can conclude that the actual discretetime LQG control system (33) implemented on a finite wordlength (β ≥ 8) machine with floating-point arithmetic remains stable in the presence of linear time-varying structured parameter perturbations and noise uncertainties. Due to the robust stability condition (31) only is a sufficient condition, we cannot conclude whether the actual discrete-time LQG control system (33), for wordlength β ≤ 7, is stable or not.…”

“…The rounded floating-point product of an m × n matrix W(k) and an n × 1 vector M(k) is given as follows [9][10][11]17]: …”

“…Gevers and Li [8] also dealt with the minimization of the effects of numerical errors on the performance of digital controllers. Besides, Chen and Kuo [9], Kuo et al [10] and Chou et al [11] have also studied the stability of digital control systems under finite wordlength effects. Note that only the article presented by Chou et al [11] analyzed the robust stability of linear digital control systems under both finite wordlength effects and linear time-varying parameter perturbations.…”

“…Besides, Chen and Kuo [9], Kuo et al [10] and Chou et al [11] have also studied the stability of digital control systems under finite wordlength effects. Note that only the article presented by Chou et al [11] analyzed the robust stability of linear digital control systems under both finite wordlength effects and linear time-varying parameter perturbations. The robust stability criterion of Chou et al [11] 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.…”

“…Note that only the article presented by Chou et al [11] analyzed the robust stability of linear digital control systems under both finite wordlength effects and linear time-varying parameter perturbations. The robust stability criterion of Chou et al [11] 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. But, to the authors' best knowledge, the problem of stability robustness of the discrete-time LQG system under linear time-varying structured (elemental) parameter perturbations, noise uncertainties and finite wordlength effects has not been discussed in the literature.…”