Non-conservative dissipativity and small-gain conditions for stability analysis of interconnected systems

Classical dissipativity and small-gain theory provide computationally tractable, but conservative methods to analyze stability of interconnected systems. In this paper, we propose a relaxation of the standard dissipativity and small-gain inequalities and prove that the corresponding conditions are necessary and sufficient for stability of interconnected systems. Thus, non-conservative conditions for stability of interconnected systems are obtained which are computationally tractable, as it is illustrated via a simple example. A further relaxation of the results is indicated for interconnected positive linear systems along with several other extensions.