Finite-horizon bounded H ∞ synchronisation and state estimation for discrete-time complex networks: local performance analysis

This study is concerned with the finite-horizon bounded H ∞ synchronisation and state estimation for the discrete-time complex networks with missing measurements based on the local performance analysis. First, a new local description of the bounded H ∞ synchronisation performance index is proposed, which considers only the synchronisation errors among neighbours. In addition, a more general sector-bounded condition is presented, where the parameter matrices are different for different node. Next, by establishing the vector dissipativity-like for the complex network dynamics, the H ∞ synchronisation criterion is derived in term of the locally coupled conditions for each node. These conditions implemented in a cooperative manner can judge whether the complex network reaches synchronisation. Similarly, the existence conditions for the estimator on each node are obtained, and then the estimator parameters are designed via the recursive linear matrix inequalities. Notably, these conditions on each node by cooperation among neighbours can achieve the desirable performance index. The distinctive features of the authors' algorithms are low complexity, scalability, and distributed execution. At last, two numerical examples are utilised to verify the effectiveness and applicability of the proposed algorithms.