CONTROL DESIGN FOR UNCERTAIN SINGULARLY PERTURBED SYSTEMS WITH DISCRETE TIME DELAY Bahador Makki University of Bremen, Bibliothekstrasse 1 D-28357 Bremen, Germany b.makki@uni-bremen.de Baharak Makki Department of Engineering Faculty of Technology and Science University of Agder Grimstad, Norway Baharakm@uia.no Abstract: The problem of state-feedback control design for a class of singularly perturbed systems with time delays and norm-bounded nonlinear uncertainties is studied in this paper. The system under consideration considers discrete delays in both slow and fast dynamics and norm-bounded nonlinear uncertainties. It is shown that the control gains are obtained to guarantee the stability of the closed-loop system for all perturbed parameters in terms of linear matrix inequalities (LMIs). We present an illustrative example to demonstrate the applicability of the proposed design approach. Key-Words: singularly perturbed systems; time delay; control design; LMI 1 Introduction Two-time scale systems have been intensively studied for the past three decades and a popular approach adopted to handle these systems is based on the so-called reduced technique. Singularly perturbed systems often occur naturally because of the presence of small parasitic parameters multiplying the time derivatives of some of the system states. Singularly perturbed control systems have been intensively studied for the past three decades; see, (for example, [7]-[11], [17], [22], [28]- [31]). A popular approach adopted to handle these systems is based on the so-called reduced technique [18]. The composite design based on separate designs for slow and fast subsystems has been systematically reviewed by Saksena, et al. in [22]. Recently, the robust stabilization of singularly perturbed systems based on a new modeling approach has been investigated in [12]. The stability problem (-bound problem) in singularly perturbed systems differs from conventional linear systems, which can be designed as: characterizing an upper bound 0  of the positive perturbing scalar  such that the stability of a reduced-order system would guarantee the stability of the original full-order system for all perturbed parameters [1]-[2]. It is known, by the lemma of Klimushchev and Krasovskii ([15]-[18]), that if the reduced-order system is an asymptotically stable, then this upper bound 0  always exists. Researchers have tried various ways to find either the stability bound 0  or a less conservative lower bound for 0  , see ([2], [18]-[27], [29]-[31]). Also, Shao and Rowland in [25] considered a linear time-invariant singularly perturbed system with single time delay in the slow states. Then, the research on time-scale modeling was extended to include singularly perturbed systems with multiple time delays in both slow and fast states ([20], [21]). Recently, the problem of robust stabilization and disturbance attenuation for a class of uncertain singularly perturbed systems with norm-bounded nonlinear uncertainties has been considered by Karimi and Yazdanpanah in [14]. Also, the robust stability analysis and stability bound improvement of perturbed parameter ) (  in the singularly perturbed systems by using linear fractional transformations and structured singular values approach (  ) has WSEAS TRANSACTIONS on SYSTEMS and CONTROL Bahador Makki, Baharak Makki ISSN: 1991-8763 456 Issue 12, Volume 6, December 2011