Robust Control of Nonlinear Time-Delay Systems via Takagi-Sugeno Fuzzy Models
نویسندگان
چکیده
Robust control theory is an interdisciplinary branch of engineering and applied mathematics literature. Since its introduction in 1980’s, it has grown to become a major scientific domain. For example, it gained a foothold in Economics in the late 1990 and has seen increasing numbers of Economic applications in the past few years. This theory aims to design a controller which guarantees closed-loop stability and performances of systems in the presence of system uncertainty. In practice, the uncertainty can include modelling errors, parametric variations and external disturbance. Many results have been presented for robust control of linear systems. However, most real physical systems are nonlinear in nature and usually subject to uncertainties. In this case, the linear dynamic systems are not powerful to describe these practical systems. So, it is important to design robust control of nonlinear models. In this context, different techniques have been proposed in the literature (Input-Output linearization technique, backstepping technique, Variable Structure Control (VSC) technique, ...). These two last decades, fuzzy model control has been extensively studied; see (Zhang & Heng, 2002)-(Chadli & ElHajjaji, 2006)-(Kim & Lee, 2000)-(Boukas & ElHajjaji, 2006) and the references therein because T-S fuzzy model can provide an effective representation of complex nonlinear systems. On the other hand, time-delay are often occurs in various practical control systems, such as transportation systems, communication systems, chemical processing systems, environmental systems and power systems. It is well known that the existence of delays may deteriorate the performances of the system and can be a source of instability. As a consequence, the T-S fuzzy model has been extended to deal with nonlinear systems with time-delay. The existing results of stability and stabilization criteria for this class of T-S fuzzy systems can be classified into two types: delay-independent, which are applicable to delay of arbitrary size (Cao & Frank, 2000)-(Park et al., 2003)-(Chen & Liu, 2005b), and delay-dependent, which include information on the size of delays, (Li et al., 2004) (Chen & Liu, 2005a). It is generally recognized that delay-dependent results are usually less conservative than delay-independent ones, especially when the size of delay 2
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