Dissipative analysis of linear coupled differential-difference systems with distributed delays
For control theorists, this provides an incremental extension to existing delay system analysis by generalizing the approximation basis.
This paper proposes a new method for dissipativity and stability analysis of linear coupled differential-difference systems with general distributed delays, using a broader class of approximation functions than Legendre polynomials. The method yields sufficient conditions in terms of linear matrix inequalities, with numerical examples demonstrating effectiveness.
In this paper, we present a new method for the dissipativity and stability analysis of a linear coupled differential-difference system (CDDS) with general distributed delays at both state and output. More precisely, the distributed delay terms under consideration can contain any $\fL^{2}$ functions which are approximated via a class of elementary functions which includes the option of Legendre polynomials. By using this broader class of functions compared to the existing Legendre polynomials approximation approach, one can construct a Liapunov-Krasovskii functional which is parameterized by non-polynomial functions . Furthermore, a novel generalized integral inequality is also proposed to incorporate approximation error in our stability (dissipativity) conditions. Based on the proposed approximation scenario with the proposed integral inequality, sufficient conditions determining the dissipativity and stability of a CDDS are derived in terms of linear matrix inequalities. In addition, several hierarchies in terms of the feasibility of the proposed conditions are derived under certain constraints. Finally, several numerical examples are presented in this paper to show the effectiveness of our proposed methodologies.