| dc.description.abstract | In this dissertation, several methods for a class of uncertain Takagi-Sugeno fuzzy models with time delays are proposed. Via Lyapunov theory, the asymptotical stability of delayed fuzzy systems is assured. In addition to stability issue, this
dissertation also investigates the system performances including H∞ , H2 and mixed-norm considerations.
Applying Lyapunov-Krasovskii approach rather than
Lyapunov-Razumikhin to analyzedelayed systems is the most popular method nowadays due to reason that the performance considerations can be incorporated. Moreover, the characteristics/classifications of delay time is one of the most important and interesting subjects in delayed schemes. For the sake of completeness, delay time can be classified into four categories such as
(a). fixed and known delay time,
(b). fixed but unknown delay time,
(c). time-varying delay with rate of varying less than 1,
(d). time-varying delay with rate of varying unlimited.
For discrete-time systems, Lyapunov-Krasovskii approach generates almost the same derivational techniques for case (b), (c) and (d). Similarly, for continuous-time systems, the techniques for case (a), (b) and (c) are the same. Therefore, the discussions of delay systems are organized in four parts such as
1. discrete-time systems with fixed and known delay time,
2. discrete-time systems with varying or unknown delay time,
3. continuous-time systems with fixed or slow-varying delay time,
4. continuous-time systems with fast-varying delay time.
In the first case, a new method is proposed in this dissertation. Via a theoretical proof, the relaxation of our approach in comparison with existing ones is guaranteed. As for the third
case investigating the fixed or slow-varying delay time for continuous-time systems, the existing literature have a limitation on derivative of delay time being less than one. This is why slow-varying case is named after. However, this limitation is not always satisfied, or the information of it is not available at all time, especially in filtering frameworks. Therefore two approaches are offered to remove this restriction. In other words, analyzing a nonlinear system subject to fast-varying delay time is allowed. We will refer to this case as
the fourth case.
Moreover, the stabilization and estimation are also included in this dissertation.Although the state feedback controller is a typical design approach. the system states are not always
completely available, thus an idea of stabilizing systems via output signals arises and is known as static output feedback regulators. It is well known that the output feedback control is a bilinear matrix inequality (BMI) problem and that the feasible solutions can not be obtained via existing convex algorithms. A reasonable approach known as iterative LMI (ILMI) is utilized to
solve this BMI problem but the solvability may depend on the initial guess. Therefore the second method, similarity transformation, is proposed to convert the BMI problems into an LMI. Since a system with or without similarity transformation
applied does not change its stabilizability. Therefore regulators determined from transformed systems can stabilize the original systems successfully. Since dynamic output feedback controllers can be converted into static output feedback regulators via augmenting some state vectors, the proposed methods for static output feedback controls can be directly implied to dynamic controllers.
Although there are two basic types of filters, the Luenberger H∞ filters are more robust than the Kalman-type since the advantage of using a Luenberger filter in comparison with a Kalman filter is that the former needs no statistical assumption on the exogenous signals. Therefore a Luenberger filter is employed in this dissertation to achieve our objectives in the filtering problems.
Since nonlinear systems can be exactly represented by a class of Takagi-Sugeno fuzzy models with norm-bounded parametric uncertainties, the proposed approaches can directly be extended to stabilize/estimate such retarded nonlinear systems. | en_US |