Consensus of discrete-time second-order multiagent systems based on infinite products of general stochastic matrices

Traditionally, the consensus of a discrete-time multiagent system (MAS) with a switching topology is transformed into the convergence problem of the infinite products of stochastic matrices, which can be resolved by using the Wolfowitz theorem. However, such a transformation is very difficult or even impossible for certain MASs, such as discrete-time second-order MASs (DTSO MASs), whose consensus can only be transformed into the convergence problem of the infinite products of general stochastic matrices (IPGSM). These general stochastic matrices are matrices with row sum 1 but their elements are not necessarily nonnegative. Since there does not exist a general theory or an effective technique for dealing with the convergence of IPGSM, establishing the consensus criteria for a DTSO MAS with a switching topology is rather difficult. This paper concentrates on the consensus problem of a class of DTSO MASs and develops a method to cope with the corresponding IPGSM. Moreover, it is pointed out that the method for these DTSO MASs can also be easily extended to deal with a large class of discrete-time MASs, including high-order MASs with a switching topology and discrete-time MASs without velocity measurements.