Radiology

Mathematics

Algorithm

Statistics

Matrix (chemical analysis)

Mathematical optimization

Artificial intelligence

Composite material

Fuzzy control system

Control (management)

Weighting

Materials science

Computer science

Applied mathematics

Control theory (sociology)

Discrete time and continuous time

Fuzzy logic

Medicine

IEEE Transactions on Cybernetics

This paper is concerned with further studies on control synthesis of discrete-time Takagi-Sugeno (T-S) fuzzy systems. To do this, a novel slack variable technique, which is homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions with arbitrary degrees, is presented by developing an efficient augmented multi-indexed matrix approach. Under the framework of homogenous matrix polynomials, the algebraic properties of both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions are collected into sets of augmented multi-indexed matrices. Thus, more information about the underlying normalized fuzzy weighting functions is involved into control synthesis. Consequently, the relaxation quality of control synthesis of discrete-time T-S fuzzy systems is improved significantly. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.

Further Studies on Control Synthesis of Discrete-Time T-S Fuzzy Systems via Augmented Multi-Indexed Matrix Approach