{'fraction_non_alphanumeric': 0.022945205479452054, 'fraction_numerical': 0.00410958904109589, 'mean_word_length': 5.022680412371134, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Observer-Based Robust Control of Uncertain Fuzzy Models with Pole Placement Constraints

Practical systems are often modelled by nonlinear dynamics. Controlling nonlinear systems are still open problems due to their complexity nature. This problem becomes more complex when the system parameters are uncertain. To control such systems, we may use the linearization technique around a given operating point and then employ the known methods of linear control theory. This approach is successful when the operating point of the system is restricted to a certain region. Unfortunately, in practice this approach will not work for some physical systems with a time-varying operating point. The fuzzy model proposed by Takagi-Sugeno (T-S) is an alternative that can be used in this case. It has been proved that T-S fuzzy models can effectively approximate any continuous nonlinear systems by a set of local linear dynamics with their linguistic description. This fuzzy dynamic model is a convex combination of several linear models. It is described by fuzzy rules of the type If-Then that represent local input output models for a nonlinear system. The overall system model is obtained by “blending” these linear models through nonlinear fuzzy membership functions. For more details on this topic, we refer the reader to (Tanaka & al 1998 and Wand & al, 1995) and the references therein. The stability analysis and the synthesis of controllers and observers for nonlinear systems described by T-S fuzzy models have been the subject of many research works in recent years. The fuzzy controller is often designed under the well-known procedure: Parallel Distributed Compensation (PDC). In presence of parametric uncertainties in T-S fuzzy models, it is necessary to consider the robust stability in order to guarantee both the stability and the robustness with respect to the latter. These may include modelling error, parameter perturbations, external disturbances, and fuzzy approximation errors. So far, there have been some attempts in the area of uncertain nonlinear systems based on the T-S fuzzy models in the literature. The most of these existing works assume that all the system states are measured. However, in many control systems and real applications, these are not always available. Several authors have recently proposed observer based robust controller design methods considering the fact that in real control problems the full state information is not always available. In the case without uncertainties, we apply the separation property to design the observer-based controller: the observer synthesis is designed so that its dynamics are fast and we independently design the controller by imposing slower dynamics. Recently, much effort has been devoted to observer-based control for T-S fuzzy models. (Tanaka & al, 1998) have studied the fuzzy observer design for T-S fuzzy control systems. Nonetheless, in