On Structured Lyapunov Functions and Dissipativity in Interconnected LTI Systems
Provides theoretical foundations for analyzing stability and dissipativity in networked control systems, but is incremental as it extends known concepts to acyclic interconnections.
The paper proves that for interconnected LTI systems over an acyclic graph, the existence of an additive quadratic Lyapunov function implies each subsystem is dissipative with respect to a set of interconnection neutral supply functions, which characterize robustness to link removal.
In this paper we study connections between structured storage or Lyapunov functions of a class of interconnected systems (dynamical networks) and dissipativity properties of the individual systems. We prove that if a dynamical network, composed as a set of linear time invariant (LTI) systems interconnected over an acyclic graph, admits an additive quadratic Lyapunov function, then the individual systems in the network are dissipative with respect to a (nonempty) set of interconnection neutral supply functions. Each supply function from this set is defined on a single interconnection link in the network. Specific characterizations of neutral supply functions are presented which imply robustness of network stability/dissiptivity to removal of interconnection links.