Non-conservative stability assessment of LTI dynamics with distributed delay using CTCR paradigm

A general class of LTI feedback control systems with a distributed delay in the feedback line is taken into account. We start with a theorem which states the equivalence of a general class of distributed delay system to a discrete delay system with multiple independent delays. While this connection has been recognized earlier, what is interesting and novel to this study is the deployment of a paradigm called The Cluster Treatment of Characteristic Roots (CTCR) for this class of systems. CTCR exhaustively declares the stability outlook of the system in the space of the delays. This capability forms a very important basis over which we can build further research connected to systems with distributed delays.