Internal stability of interconnected systems

Abstract

In this paper, internal stability of interconnected systems is considered. It is shown that a system consisting only of single-input/single-output (SISO) plants is internally stable if and only if ΔΠipi(s) has all its roots in the open left half of the complex plane, where pi(s) are the denominators of the plant transfer functions and Δ is the system determinant same as in the Mason's formula. This theorem is also extended to the case where the system may have multi-input and/or multi-output plants. Several typical control schemes are employed as illustrative examples to demonstrate the simplicity and usefulness of these results in internal stability analysis and stabilization synthesis.