Dissipative Stability Conditions for Linear Coupled Differential-Difference Systems via a Dynamical Constraints Approach
Provides a theoretical extension of stability analysis tools to a specific class of hybrid systems, but the contribution is incremental as it generalizes existing methods without demonstrating practical advantages or numerical results.
The paper derives dissipative stability conditions for linear coupled differential-difference systems using a Krasovskii functional and slack variables, generalizing the Finsler Lemma approach from LTI systems. The proposed method is shown to be equivalent to direct trajectory substitution.
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 $\dot{\bm{x}}(t)$, similar to the case of LTI system.