Eigenvalue analysis based control scheme for interconnected autonomous systems

The paper proposes a simple decentralized control scheme to address stability problem of interconnected systems. Sufficient condition for stability of closed loop system is derived using contraction theory based analysis. Here, the conditions for stability are reflected in terms of bounds on strengths of interconnections. The uniform negative definiteness of associated Jacobian of the system in differential framework is ensured by identifying the location of eigenvalues using Gerschgorin theorem. Results are verified by considering an interconnected system with individual subsystems having interaction with their nearest neighbours.