Dissipative Stability Conditions for Linear Coupled Differential-Difference Systems via a Dynamical Constraints Approach

In this short note, we derive dissipative conditions with slack variables for a linear coupled differential-difference (CDDS) via constructing a Krasovskii functional. The approach can be interpreted as a generalization of the Finsler Lemma approach for standard LTI systems proposed previously in \cite{de2001stability}. We also show that the proposed slack variables scheme is equivalent to the approach based on directly substituting the system trajectory $\dot{\mathit{x}}(t)$, similar to the case of LTI system.