A memory state-feedback control method for multi-agent systems on time scale: Applications to circuit networks

Abstract

 This paper proposes a novel memory state-feedback control (MSFC) strategy for multi-agent systems (MASs) operating on time scales. The communication topology is modeled by a collection of directed graphs with switching edges. We analyze the exponential stability of the error dynamics within a leader-follower synchronization framework, crucial for MAS control. Employing linear matrix inequalities (LMIs) and Lyapunov-Krasovskii functionals (LKFs), we establish sufficient conditions to guarantee global exponential stability for the considered systems. Notably, the synchronization conditions for MASs on different time scales differ from those on discrete or continuous time scales alone. This approach allows for a unified framework encompassing both discrete and continuous-time global synchronization problems. Finally, a simulation study utilizing a neural network (NN)-based circuit model demonstrates the effectiveness of the proposed control design.