Input-output stability of composite feedback systems

A new criterion for input-output stability of multiloop systems is presented. The setting proposed by Zames is employed and emphasis is placed upon the multiloop structure of the system. The criterion is derived from the result by Zames and includes, as a special case, some of the previous results about interconnected systems reported by Tokumaru et al., Porter and Michel, and Cook. The criterion is especially useful when applied to multiinput-multioutput feedback systems which have a time-invariant linear system in the forward path and a time-varying nonlinear diagonal gain in the feedback path. It is simpler than, and in certain cases sharper than, the standard multivariable circle criterion.