Generalized structure for stable model reference adaptive control system

Only a conservative stability condition of the robust model reference adaptive control system (MRACS) was obtained in the past typical studies as since the stability of robust MRACS had been analyzed by an algebraic approach that recursively evaluates the L_2δ norms of signals. Furthermore, that approach seems to be considerably different compared with an analysis technique for a general nonlinear control system because it hardly uses the structural feature of the feedback system. Consequently, it seems that the derived stability condition does not offer how the stabilization of robust MRACS is essentially achieved, and also it does not provide an information enough to realize a robust MRACS which has sufficient stability margin and better control performance. To solve such problems, this paper reveals an equivalent feedback system to the main loop of robust MRACS, and derives a more tight stability condition by using the notion of finite-gain L_2δ stability. The results of this paper seem to be useful for an understanding of its stabilization mechanism, and the realization of the robust MRACS with considering a sufficient stability margin and better control performance.