Stability analysis of digital Kalman filters with floating-point computation

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

“…It is reasonable to assume that the values of the nominal matrices A and B here are retrieved from memory when they are needed. Thus these values have already been rounded to exact values of the nominal matrices A and B (Kuo, 1980;Kuo et al, 1991;Kuroe and Okada, 1992). In order to obtain the feedback gain matrix F, we must solve the algebraic Riccati Eq.…”

“…The rounded floating-point product of a m×n matrix N(k) and an n×1 vector M(k) is given as follows (Wilkinson, 1963;Chen and Kuo, 1989;Kuo et al, 1991): …”

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

“…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.…”

“…The digital controller and the Kalman-Bucy filter are realized with floating-point arithmetic. Quantization errors occur only when: (i) the system output y(t) of the real, controlled continuous-time plant is converted into the actual digital signal fl[y * (k)] by an analog-to-digital converter on a floating-point computer, and (ii) the system matrices A * , B * , C * , the feedback gain matrix F * , the estimator gain H * , the controller u * (k) = −fl[F * x * (k)] and the Kalman-Bucy filterx * (k+1) = fl[fl[fl[A * x * (k)]+fl[B * u * (k)]]+ fl[H * fl[fl[y * (k)] − fl[C * x * (k)]]]] are calculated with floating-point computation and finite wordlength on a digital computer[10,15,16].…”