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 differentialdifference (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 de Oliveira & Skelton (2001). We also show that the proposed slack variables scheme is equivalent to the approach based on directly substituting the system trajectory ẋ(t), similar to the case of LTI system.