Study On Fuzzy Control For Nonlinear Time-delay Systems

Time delay can be found in various engineering systems such as chemical processes, biological systems, and economic systems. Compared to the systems without delay, it is frequently a source of instability and a source of generation of oscillation in many control systems. Therefore, the study of time delay is indispensable and possesses great significance. The development of modern mathematics, control theory and computer technology provides a powerful tool for the study of uncertainty time delay systems. As an active research field, the nonlinear system theory made a rapid progress recently, especially in introducing differential geometry, which plays an important role in nonlinear system theory. However as a more common problem and a more difficult problem, the study of nonlinear time delay systems did not get considerable attention. Recently, fuzzy systems are successfully applied to many control problems because they need not accurate mathematical models of the system and can cooperate with human experts' knowledge. Furthermore, the controller design is easy in fuzzy control techniques, which is the same with many nonlinear systems and has strong robust characteristic. Since 80's 20th century, the fuzzy control obtains great development in control theory and engineering.Accordingly, based on fuzzy control technique, the purpose of this dissertation is to study robust control for nonlinear time delay systems. The main works is generalized as follows:Based on fuzzy Takagi-Sugeno (T-S) model, fuzzy control and stability analysis for a class of uncertain time-delay systems are presented. First, the fuzzy T-S model is used to approximate time-delay systems with uncertainty. Then by LMI approach, robust stabilizations for fuzzy system are proposed under the condition that the system is observable and unobservable, respectively. Essential idea is to divide the state space inton fuzzy subspace. In every fuzzy subspace, the uncertain fuzzy T-S model is used to present local linear systems with uncertainty. The local robust observer and state feedback controller are designed for very local linear systems with uncertainty. Global robust observer and state feedback controller are average summation of local subsystem...