Decentralized control for arbitrarily interconnected systems over lossy network

This paper deals with the control of arbitrarily topological interconnected systems where information communicated between subsystems may be lost due to unreliable links. First, the stochastic variable that is responsible for the communication status of lossy network is regarded as a source of model uncertainty. The system is modeled in the framework of linear fractional transformation with a deterministic nominal system and a stochastic model uncertainty. Then, the robust control theory is employed for system analysis. The largest probability of communication failure, tolerated by the interconnected systems keeping mean square stable, can be obtained by solving a μ synthesis optimization problem. Decentralized state feedback controllers are designed to ensure that the whole system is mean square stable for a given communication failure rate, based on the technique of linear matrix inequalities. An illustrative example is presented finally to verify the effectiveness of the proposed model and method.