Fuzzy Control Systems Stability: Time and Frequency Domain Criteria

Abstract

Stability is the most important attribute of any system. A prerequisite for all stability criteria of control systems is the existence of a mathematical model. In contrast. fuzzy control systems are often designed based on heuristic human knowledge and without a mathematical model, hence, it has been a difficult task to determine stability of fuzzy control systems under such restrictions. This paper uses the Takagi/Sugeno type of fuzzy rules whose consequences are analytical, and singletons are used as a basis for a number of sufficiency conditions for stability. The schemes considered here are time-domain, but a brief survey which proceeds the main results considers frequency domain as well. Both Lyapunov and interval matrix criteria are presented with some proofs and numerical examples.