Analysis of Controllability, Observability and Stabilization for a Class of Systems Described by Takagi-Sugeno Fuzzy Models by means of Fuzzy Pole Assignment

Abstract

The present work is concerned to solve the problem of nonlinear robotic control systems on the basis of Takagi-Sugeno (T-S) fuzzy models. In addition, controllability and observability studies for T-S fuzzy model systems are considered for Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) systems. In particular, the robust pole assignment approach is extended to the fuzzy field. This approach
is used to design fuzzy stabilizers and fuzzy observers directly on the overall T-S fuzzy system, which is the representation of the nonlinear robotic system obtained from the weighted sum of local linear subsystems. The suggested method is considered for either SISO or MIMO systems. Furthermore, the method allows inducing an arbitrary behavior into the fuzzy plant in a relatively easy way. Two examples are used to verify the effectiveness of the proposed approach. The results are compared with the well-known Parallel Distributed Compensation (PDC) method, which
is designed on the basis of Linear Matrix Inequalities (LMIs).