Stability Analysis of Linear Coupled Differential-Difference Systems With General Distributed Delays

Abstract

We present a new approach for the stability analysis of linear coupled differential-difference systems (CDDS) with a general distributed delay. The distributed delay term in this note can contain any L 2 function which is approximated via a class of elementary functions including polynomial, trigonometric and exponential functions etc. Through the application of a new proposed integral inequality, sufficient condition for the stability of the system is derived in terms of linear matrix inequalities based on the construction of a Liapunov Krasovskii functional. The methods proposed in this note can handle problems which cannot be deal with by existing approaches. Two numerical examples are presented to show the effectiveness of our proposed stability condition.

Stabilisation of distributed time-delay systems: a smoothed spectral abscissa optimisation approach

“…Stabilization of systems with distributed delays can be carried out via both frequency and time-domain approaches. Within the first approach, one can find, for instance, the characterization of stability crossing curves, (Morȃrescu, Niculescu, & Gu, 2007), or the quasi-continuous pole placement methodology, (Michiels, Vyhlídal, & Zítek, 2010), whereas within the second approach, one mostly finds results based on the solution of Linear Matrix Inequalities (LMIs), see, e.g., (Chen & Zheng, 2007;Feng, Nguang, & Perruquetti, 2020;Feng, Nguang, & Seuret, 2019;Liu, Fridman, Johansson, & Xia, 2016;Liu, Seuret, Xia, Gouaisbaut, & Ariba, 2019;Xie, Fridman, & Shaked, 2001;Zheng & Frank, 2002). Results based on the so-called delay Lyapunov matrix are also reported in (Juárez, Alexandrova, & Mondié, 2020), (Mondié, Ochoa, & Ochoa, 2011), (Egorov, Cuvas, & Mondié, 2017).…”

Periodic consensus in network systems with general distributed processing delays

“…The case of discrete delay is always viewed as a delay with Bernoulli distribution. Mathematically, there have been many contributions to the stability of network system with processing delays, see [3,14,15] for examples.…”

“…That is,ẏ i (t) = 0 for i = 1, 2, • • • , n 0 , and y * (t) solves the equation (3). And then the characteristic equation h 0 (z) = 0 becomes…”

“…where p i is the algebraic multiplicity of µ i , m 0 is the number of the different eigenvalues of P 0 . Let S * (t) be a fundamental solution operator of the equation (3). Then the solution X(t) of the equation 10becomes…”

The development of university foundations in China

“…The construction of Krasovskiȋ functionals (KF) in timedomain [16] has increasingly become an effective strategy for the stability analysis and state estimation of LTDSs [17], [18], where the stability (synthesis) conditions are denoted as semidefinite programming (SDPs) problems [19]. The conservatism of this approach is mainly affected by the complexity of the underlying delay systems, the generality of the predetermined form of KFs [16], and the integral inequalities employed to construct them.…”