Non–conservative and tractable stability tests for general linear interconnected systems with an application to Power Systems

Existing Lyapunov methods for verifying stability of linear interconnected systems provide either non–conservative but non–tractable global conditions, or tractable but conservative local conditions. In this paper we provide non–conservative and tractable stability tests for general linear interconnected systems. Firstly, we exploit the concept of a finite–time Lyapunov function to derive a global stability test that can be implemented efficiently by parallelization. Secondly, the same concept is further employed to derive local, dissipativity–type conditions, that can be formulated as a set of distributed linear matrix inequalities. Thirdly, an assessment of all stability tests for linear interconnected systems in terms of complexity, scalability and applicability is performed. The usefulness of the developed stability tests for real–life applications is illustrated on benchmark power system networks.