This paper discusses the robust filtering problems for linear discrete-time systems with polytopic parameter uncertainty under the H2 and H , performance. We aim to derive a less conservative design than existing sufficient Iinear matrix inequality (LMI) based conditions. It is shown that a more efficient evaluation of robust HZ or H , performance can be obtained by a matrix inequality condition which contains additional free parameters as compared to existing characterizations. When applying this new matrix inequality condition to the robust filter design, these parameters give additional freedoms in optimizing the guaranteed H2 or H , performance.The optimization will then lead to a less conservative design. The results will recover the existing robust HZ and H , filtering ones when the additional free parameters are set to be zero. We also propose an iterative algorithm to further refine the suboptimal filter. Examples are given to demonstrate the less conservatism of the proposed approaches.

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This paper studies the consensus problem for a class of general second-order multi-agent systems (MASs) with communication delay. We first consider the delay-free case and obtain a necessary and sufficient condition for consensus. Then, based on the obtained conditions for the delay-free case, we deduce an explicit formula for the delay margin of the consensus for the case with time delay using the relationship between the roots of the characteristic equation and the time delay parameter. In addition, we consider the special case where the second-order model is a double integrator. For this case, simpler consensus conditions under communication delay are provided.

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