Consensus control of discrete-time multi-agent systems with time-delays and multiplicative measurement noises
Scientia Sinica Mathematica · 2016
This work is concerned with stochastic consensus conditions of discrete-time multi-agent systems with time-delays and multiplicative measurement noises. By the algebraic graph theory and the matrix theory, the stochastic consensus problem is converted into the stochastic stability problem of discrete-time stochastic delayed systems driven by multiplicative noises. Then by establishing the stochastic stability criteria for discrete-time stochastic delayed systems, the stochastic consensus conditions are deduced. For the case with first-order dynamics, the sufficient conditions for the mean square and the almost sure strong consensus are deduced under balanced digraphs. For the case with second-order dynamics, the consensus analysis is given under undirected graphs, and it is proved that for any given bounded time-delay and noise intensity, the stochastic weak consensus for the position and stochastic strong consensus for the velocity can be achieved by carefully choosing the control gains. These consensus results are further extended to the leader-following case.