Robust admissible consensus of singular multi-agent systems using sliding mode approach

The admissible consensus problem of singular multi-agent systems (SMASs) with mismatched norm-bounded parametric uncertainties and unknown norm-bounded disturbances is investigated by an integral sliding mode technique. Under a directed spanning tree network of the state transmission graph, the error states are defined. Then a linear matrix inequality (LMI)-based sufficient condition is presented to guarantee regularity, free impulse, quadratic stability and H-infinity performance of the sliding mode dynamics of the error states. Next, an integral sliding manifold parameter is designed to decrease the order of the LMI caused by the parametric uncertainties, and matrix inversion formulas and inequality techniques are applied to reduce the conservativeness of the LMI. Finally, the control laws, relying on the error states, the property of the state transmission graph and the upper norm bound of disturbances, are presented to ensure the state trajectories of the resulting closed-loop system to achieve robust admissible consensus with H-infinity performance. A simulation example is provided to show the effectiveness of the proposed method.