Robust Stability Measures for Discrete-Time Linear Regulators with Computational Delays.

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

“…On the other hand, if the wordlength W is infinite and if we do not consider the computational delay, the presented sufficient condition (22) can be reduced to the result of Chou (1995). That is, the results of Chou (1995) and Chen et al (1997) are special cases of the proposed condition (22). Here it should be noted that Chou (1995) and Chen et al (1997) have shown that their proposed non-Lyapunov conditions are less conservative than the existing robust stability conditions presented in the past decade.…”

“…Remark 2: If the wordlength (mantissa length) W is infinite, the linear time-varying uncertainty matrix E (k) can be reduced to the linear time-varying perturbation matrix E(k) and the non-Lyapunov sufficient condition (22) can be reduced to the result of Chen et al (1997). On the other hand, if the wordlength W is infinite and if we do not consider the computational delay, the presented sufficient condition (22) can be reduced to the result of Chou (1995).…”

“…Therefore, issues related to discrete-time linear control systems with computational delays have been extensively studied (see, for example, Mita, 1985;Ishihara, 1988;Kolla and Farison, 1990;Ha et al, 1993;Yang, 1994;Chen et al, 1997;and references therein). Here it should be noted that only a few articles (Ishihara, 1988;Kolla and Farison, 1990;Chen et al, 1997) addressed the problem of robust stability of discrete-time linear control systems with computational delays. Ishihara (1988), Kolla and Farison (1990) and Chen et al (1997) reported bounds for linear time-varying parameter perturbations of discrete-time linear regulators with computational delays, respectively.…”

“…Here it should be noted that only a few articles (Ishihara, 1988;Kolla and Farison, 1990;Chen et al, 1997) addressed the problem of robust stability of discrete-time linear control systems with computational delays. Ishihara (1988), Kolla and Farison (1990) and Chen et al (1997) reported bounds for linear time-varying parameter perturbations of discrete-time linear regulators with computational delays, respectively. On the other hand, discrete-time control systems are normally designed under the assumption that both the system states and the controller gains have an arbitrary, large wordlength.…”

Model predictive control of nonlinear systems: Computational burden and stability

“…If the computation delay is too large, the proposed MPCGS has less robustness against uncertainties and disturbances. How to analyse the robust stability of the closed-loop system with computational delay is an interesting subject and some results have been presented, for example see Chen et al (1997), Chen and Gu (1991). However it is beyond the scope of this paper.…”