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

TL;DR

This paper introduces new dissipative stability conditions for linear coupled differential-difference systems using a Krasovskii functional and slack variables, generalizing existing methods for LTI systems.

Contribution

It presents a novel approach with slack variables for stability analysis of CDDS, extending the Finsler Lemma methodology to more complex systems.

Findings

Derived dissipative conditions with slack variables for CDDS.

Showed equivalence to direct substitution approach for system trajectories.

Generalized Finsler Lemma approach for differential-difference systems.

Abstract

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.