Designing Distributed Impulsive Controller for Networked Singularly Perturbed Systems

This paper develops a novel synthesis approach for synchronization of a network of singularly perturbed systems (SPSs) with a small singular perturbation parameter (SPP) ε via distributed impulsive control. First, a decoupling method in the setting of directed networks is employed to decompose networked SPSs related to complex eigenvalues of the Laplacian matrix. Then, based on an improved piecewise continuous Lyapunov function, an ε-dependent synchronization criterion is established. The relationship among the impulse interval, the impulse gain matrix and ε is revealed. By employing the newly-obtained synchronization criterion, sufficient conditions on the existence of an ε-dependent impulse gain matrix are derived. Finally, an example is simulated to verify the effectiveness of the theoretical results. © 2022 IEEE.