Sparsely distributed sliding mode control for interconnected systems

This paper proposes a framework for the design of sparsely distributed output feedback discrete-time sliding mode control (ODSMC) for interconnected systems. The major target here is to develop an observer based discrete-time sliding mode controller employing a sparsely distributed control network structure in which local controllers exploit some other sub-systems' information as well as its own local information. As the local controllers/observers have access to some other sub-systems' states, the control performance will be improved and the applicability region will be widened compared to the decentralised structure. As the first step, a stability condition is derived for the overall closed-loop system obtained from applying ODSMC to the underlying interconnected system, by assuming a priori known structure for the control/observer network. The developed LMI based controller design scheme provides the possibility to employ different information patterns such as fully distributed, sparsely distributed and decentralised patterns. In the second step, we propose a methodology to identify a sparse control/observer network structure with the least possible number of communication links that satisfies the stability condition given in the first step. The boundedness of the obtained overall closed-loop system is analysed and a bound is derived for the augmented system state which includes the closed-loop system state and the switching function.