FINITE STABILITY REGIONS FOR LARGE-SCALE SYSTEMS WITH STABLE AND UNSTABLE SUBSYSTEMS.

Algebraic criteria are derived to determine finite regions of asymptotic stability of time-varying non-linear large-scale systems composed of exponentially stable (unstable) subsystems. The interconnections among the subsystems can be arbitrary; sign-negative coupling is allowed. The approach uses a composite system Lyapunov function consisting of subsystem Lyapunov functions. The stability tests are confined to a bounded region of interest and theorems are given to check if this region is a region of asymptotic stability or if at least some smaller stability region exists. Two examples illustrate the method and demonstrate its superiority over previous works.