Dissipation inequalities for distributed systems on graphs

This paper considers linear dynamic systems with an interconnection structure specified by a directed graph. We formulate linear matrix inequalities for computation of performance of the system based on dissipation inequalities, and define a notion of local dissipation. We derive a computational test for this which may be solved via semidefinite program. The structure of the resulting matrix inequalities is related to recent approaches to distributed control, and the results of this paper reduce to recent results in the case where the underlying graph structure is a rectangular array. Based on the analytical result, a state feedback synthesis approach is presented and it also can be cast as a semidefinite program.