Observers and controllers for Takagi-Sugeno fuzzy systems

Sammanfattning: This thesis studies analysis and design issues for observers anc controllers for Takagi-Sugeno (TS) fuzzy systems. Many physical systems are nonlinear in nature and using the well known linear techniques for such systems may result in bad performance, and even instability. On the other hand, analysis and design of observers and controllers for general nonlinear systems tend to be a quite involved procedure. It turns out, however, that a TS fuzzy system is able to represent or approximate a large class of nonlinear systems. Developing methods for observation and control for TS systems should therefore be worthwile. The TS fuzzy systems considered in this thesis are allowed to have an affine term. This can be an advantage, because affine TS fuzzy systems may be able to approximate nonlinear functions  to high accuracy with fewer rules than the TS fuzzy system with linear consequents only. It is shown that observer design is more difficult when the weights in the TS fuzzy systems depend on the estimated state, and an explicit design procedure is devised for that case. A reduced order observer is also proposed. To deal with modeling errors a fuzzy sliding mode approach is taken. The controller design is focused on affine TS fuzzy systems. Analysis and design of observer-based error state feedback controllers are proposed. Furthermore, it is also shown how recent results on classical gain scheduling may be used for control of affine TS fuzzy systems. Analysis and design for both observers and controllers are based on quadratic stability analysis, and in some cases, on robust quadratic stability analysis. Although this approach may be conservative, it often results in automatic design procedures based on optimization subject to linear matrix inequalities.