An approach to stability analysis of second order fuzzy systems

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Abstract
The stability of fuzzy systems can be discussed by the theorem of K. Tanaka and M. Sugeno (1990). However, it is difficult to find the common positive definite matrix P which is introduced in the theorem, and satisfies, for example, two Lyapunov inequalities A/sub 1//sup T/PA/sub 1/-P<0 and A/sub 2//sup T/PA/sub 2/-P<0. The authors present a new simple approach for finding the whole region where a 2*2 real matrix P exists. As an example, two spring-mass physical systems with damping are treated, and the region of P is obtained. Also, three examples considered by Tanaka and Sugeno are discussed. It is emphasized that illustrating the P-region calculated by the approach aids the design of a fuzzy controller.

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