d m

ed ix la ba um Recently, control problems of singularly perturbed systems have attracted considerable attentions (see [11–19] and the references therein). Based on the small-gain theorem, [20] studies robust stability problem for continuous-the literature, which undoubtedly is very important for the applications of singularly perturbed system theory. This paper is concerned with the problem of designing H1 state feedback controller for discrete-time singularly d of singu-prescribed ed. First, a e of singu-considered prescribed the upper ised eigen-n methods perturbed the bound Finally, an ltaneously a discrete-2 presents Section 3, 1141and discrete-time singularly perturbed systems by a unified state-feedback design. In [21], the possibilities of sliding mode control design for synchronous generators are analysed for singularly perturbed systems. Stability analysis and robust controller design of uncertain discrete-time singularly perturbed systems are considered in [22]. Based on Riccati equation approach, unified H1 approaches are given in [23] perturbed systems, and how to improve the boun lar perturbation parameter e, subject to meeting a performance bound requirement being consider method is given for evaluating the upper bound larly perturbed parameter e, subject to the system with a designed controller to be with a performance bound for e [ (0, e], where bound e can be obtained by solving a general value problem (GEVP) [32]. Secondly, desig for H1 controller of discrete-time singularly systems without the consideration of improving of e is given in terms of solutions to LMIs. LMI-based approach is presented for simu designing the bound of e and H1 controller for time singularly perturbed system. This paper is organised as follows. Section system description and some preliminaries. I