Hierarchical distributed control of a class of interconnected jump Semi-Markov linear systems

In this paper, an extension of interconnected discrete-time jump Markov systems (JMS) with different sampling time of the continuous dynamics and the underlying Markov chain is considered. In particular, it is assumed that the sampling time of the Markov chain is a multiple of the sampling time of the continuous part of the dynamics. In contrast to classical JMS [2], this model class allows one to account for small time constants in the continuous part of the dynamics, while simultaneously modeling abrupt stochastic changes in the system behavior on a coarser time-scale. For the proposed system class, which can also be considered as a special case of jump Semi-Markov systems (JSMS) [18], the design of a distributed two-layer state-feedback controller is presented. In order to adjust the structure of the distributed controller to the inherent interconnection topology of the system, a structural analysis is performed prior to the control design, and the subsystems are grouped into clusters. As an additional benefit, the grouping of subsystems significantly reduces the combinatorial complexity when it comes to a simultaneous design of the distributed controller and the underlying communication topology.