An approach to stability analysis of second order fuzzy systems

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 A₁^TPA₁-P <0 and A₂^TPA₂-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