Stability analysis of large-scale systems with stable and unstable subsystems

Abstract

Sufficient conditions are given for both exponential and asymptotic stability of time-varying non-linear large-scale systems composed of stable and unstable subsystems. Sign-negative coupling among the subsystems, which can be of arbitrary order and interconnected in arbitrary fashion, is allowable. Under the conditions the required stability property of the overall system is implied by the stability properties of all its subsystems and global features of their interactions. The interactions can be expressed in terms of time-varying, sign-indefinite functions rather than only in terms of time-invariant positive definite functions. Three examples are worked out to illustrate application of- the results.