This paper investigates a fundamental problem of stabilization for time-varying multiplicative noise stochastic systems. A necessary and sufficient stabilization condition is presented based on the receding horizon approach. The explicit time-varying controller is designed if the condition is satisfied. The presented results are new to the best of our knowledge.
This paper studies the consensus problem for discrete-time multi-agent systems of first-order in the presence of constant communication delay. Provided that the agent dynamics is unstable and the network topology is undirected, effects of two kinds of communication delays on consensus are investigated.When the relative information is affected by delay, we show that the effect of delay can be alleviated by using the historical input information in the protocol design. On the other hand, if the communication delay only influences the actually transmitted information, sufficient condition admitting any large yet bounded delay for consensus is obtained, and the delay in this case is allowed to be unknown and time-varying. Finally, simulation results are provided to demonstrate the effectiveness of the theoretical results.
