On the exponential leader-tracking control for high-order multi-agent systems via distributed PI strategy in the presence of heterogeneous time-varying delays

This paper deals with the exponential leader-tracking consensus control problem of high-order Multi-Agent Systems (MASs) sharing information via a non-ideal communication network. To emulate a more realistic environment, a specific time-varying delay has been associated with each communication link within the network, whose value, at each time instant, depends on the real conditions of the communication channel. To solve this problem, a fully-distributed delayed Proportional-Integral (PI) control protocol able to guarantee the exponential stability of the entire delayed closed-loop MAS is proposed. The stability of this latter is analytically proved by exploiting Lyapunov-Krasovskii theory combined with Halanay Inequality, thus obtaining exponential stability conditions expressed as a feasible Linear Matrix Inequality (LMI) problem. Exemplary numerical simulations corroborate the effectiveness of the theoretical derivation.