A Parallelizable Algorithm for Stabilizing Large Sparse Linear Systems With Uncertain Interconnections

Abstract

This paper proposes a new method for permuting sparse matrices into an upper block triangular from. The algorithm is highly parallelizable, which makes it suitable for large-scale systems with uncertain interconnection patterns. In such cases, the proposed decomposition can be used to develop flexible decentralized control strategies that produce a different gain matrix whenever the configuration changes. Applications to interconnected microgrids and supply and demand networks are provided to illustrate the versatility of the proposed approach.

Keywords

• Large-scale systems
• reconfigurable interconnections
• uncertainty
• decentralized control
• sparse matrices
• block triangular structure