A New Mathematical Criterion for Exponential Function Projective Synchronization and Guaranteed Cost Controller of Complex Dynamical Networks

This paper addresses cost-constrained synchronization control in complex dynamical networks (CDNs) with mixed time-varying delays, asymmetric couplings, and multi-connections. A novel criterion for exponential projective synchronization and guaranteed-cost control is developed using the Lyapunov–Krasovskii functional method, extended reciprocally convex and free-matrix-based inequalities, and LMIs. The proposed scheme reduces the cost upper bound via a new quadratic cost function. A numerical example illustrates the effectiveness of the approach.