New approaches to relaxed quadratic stability condition of fuzzy control systems

TLDR

The paper proposes two relaxed quadratic stability conditions for fuzzy control systems. The authors introduce a first condition using the S‑procedure to exploit premise information, and a second condition that aggregates subsystem interactions into a single matrix solved by linear matrix inequalities. The study demonstrates that the second condition subsumes conventional stability criteria and, through examples and simulations, confirms the effectiveness of the proposed conditions.

Abstract

This paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures. Two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems. The first one employs the S-procedure to utilize information regarding the premise parts of the fuzzy systems. The next one enlarges the class of fuzzy control systems, whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality. The relationships between the suggested stability conditions and the conventional well-known stability conditions reported in the previous literatures are also discussed, and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions. Finally, some examples and simulation results are presented to illustrate the effectiveness of the stability conditions.