Internal stability of interconnected systems

In this paper, internal stability of interconnected systems is considered. It is shown that a system consisting only of single-input/single-output (SI SO) plants is internally stable if and only if Delta Pi(i)p(i)(s) has all i ts roots in the open left half of the complex plane, where p(i)(s) are the denominators of the plant transfer functions and Delta is the system determ inant same as in the Mason's formula. This theorem is also extended to the case where the system may have multi-input and/or multioutput plants. Sever al typical control schemes are employed as illustrative examples to demonst rate the simplicity and usefulness of these results in internal stability a nalysis and stabilization synthesis.