State estimation of stochastic singularly perturbed discrete-time systems

✍ Scribed by Hisashi Kando

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 360 KB
• Volume: 18
• Category: Article
• ISSN: 0143-2087
• DOI: 10.1002/(sici)1099-1514(199701/02)18:1<15::aid-oca586>3.0.co;2-t

✦ Synopsis

Studies on discrete-time system analysis and design via singular perturbations and time-scale methods have been developed in recent years. Representative issues and results of modelling, analysis and control have been reviewed by Naidu et al. These studies can be classified into the slow-time-scale version 2 -7 and the fast-time-scale version. 8 -11 In the single-rate version described above, performance degradation between continuous-time and sampled-data systems is inevitable (slow-time-scale version) and the computation time of the control law cannot be neglected (fast-time-scale version). In order to alleviate these difficulties, multirate design methods have been developed on the basis of singular perturbations and time-scale methods by Litkouhi and Khalil 12 and Kando and Iwazumi. These studies are focused on deterministic discrete-time systems.

On the other hand, stochastic control and estimation problems of singularly perturbed systems have been extensively developed by many researchers 15 for continuous-time systems. With regard to examples of such stochastic control and estimation problems, we can quote Khalil and Gajic 16 and Kokotovic et al. For discrete-time systems, stochastic problems of singularly perturbed systems have been treated recently by Rao and Naidu, Gajic and Shen and Lim et al. The computational aspects of the Kalman filter of the slow-time-scale version have been investigated in Reference 18. The prediction-type Kalman filter of the fast-time-scale version has been considered by using the parallel algorithm and the closed-loop transformation.