Stability analysis and design of fuzzy control systems

An introductory survey of fuzzy control

Addresses the issue of stability of a fuzzy system described by fuzzy rules with singleton consequents. It first presents two canonical forms of a fuzzy system: a parametric expression and a state-space expression. A fuzzy system with singleton consequents is found to be a piecewise-polytopic-affine system. Then the paper gives stability theorems for a discrete-time system as well as for a continuous time system. It also gives a brief survey on the stability issues of fuzzy control systems.

On stability of fuzzy systems expressed by fuzzy rules with singleton consequents

Paper: A control engineering review of fuzzy systems

Theoretical and linguistic aspects of the fuzzy logic controller

This paper considers the difficulties which arise from an attempt to analyse fuzzy systems. Previous work in this area is briefly reviewed and a new way of describing closed-loop fuzzy systems is introduced. Using only finite discrete fuzzy relations, it is possible to define such concepts as state equivalence, stability and controllability, and, by restricting attention to a special class of systems, a simple control problem can be solved. The basic ideas discussed in the paper are, perhaps, the first steps towards a practical theory of fuzzy systems.

R. M. Tong

Papers

Analysis and control of fuzzy systems using finite discrete relations