Open AccessExponential input‐to‐state stability of delay reaction‐diffusion systems
Author(s) -
Ren MengZhen,
Liu XiaoZhen,
Wu KaiNing
Publication year - 2021
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/cth2.12088
Subject(s) - exponential stability , diffusion , control theory (sociology) , boundary (topology) , stability (learning theory) , term (time) , state (computer science) , mathematics , exponential function , reaction–diffusion system , property (philosophy) , ordinary differential equation , computer science , control (management) , differential equation , mathematical analysis , algorithm , physics , quantum mechanics , nonlinear system , artificial intelligence , machine learning , thermodynamics , philosophy , epistemology
This brief paper considers the exponential input‐to‐state stability (EISS) for delay reaction‐diffusion systems (DRDSs). The distributed input and boundary input are both included in the considered model. Boundary input is an important characteristic for DRDSs which are a kind of partial differential systems. Using Lyapunov–Krasovskii functional method and Wirtinger‐type inequality, a delay‐dependent sufficient condition is obtained to ensure the EISS of DRDSs. Besides the effect of time delay on the EISS, this sufficient condition also shows the effect of the diffusion term on the EISS and this is a significant property of reaction–diffusion systems differing from the ordinary differential systems. At last, numerical examples are provided to show the effectiveness of the theoretical results.