ABSTRACT
It is well known that a wide class of physical systems in engineering, biology, ecology, socioeconomic, nuclear, thermal and chemical processes etc. may be appropriately described by the bilinear model (Mohler 1991, Li et al. 2009, Li et al. 2008, Lee et al. 2009, Kim & Lim 2003). Whereas the above systems are usually described by high-order differential (difference) equations. It requires large number of computer memory and considerable operation time to handle such large-scale systems due to the high order dimensions of these plants. Designs of controllers for such models are costly to implement and sometimes even unrealizable. Singular perturbation methods (Kokotovic et al. 1986, Naidu 1988, Chiou & Wang 2005, Chiou 2006, Moreno-Valenzuela et al. 2008, Kim & Lim, 2007) are useful in solving problems of high dimensionality and difficulties of stiffness in dealing with large-scale systems. The composite design based on separate designs for slow and fast subsystems has been systematically reviewed (Kokotovic 1986, and Chiou 2013, 1988). Up to now, however, there was little literature concerning the stabilization problem of singularly perturbed bilinear systems. The stabilization problem of singularly perturbed strictly bilinear system is studied by using the Lyapunov theory (Tzafestat & Anagonostou 1984, Asamoah & Jamshidi 1987, extend the results of Tzafestat & Anagonostou (1984) to singularly perturbed bilinear systems, but some results (Asamoah & Jamshidi 1987) are shown to be erroneous by Li and Sun (1988). The above results appear to be restricted to the continuous-time cases. But, the relationships of state trajectories between the original systems and the reduced systems have not been discussed for the above papers.
