Open AccessFinite‐time asynchronous control for positive discrete‐time Markovian jump systems
Author(s) -
Shang Hui,
Qi Wenhai,
Zong Guangdeng
Publication year - 2019
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/iet-cta.2018.5268
Subject(s) - control theory (sociology) , controller (irrigation) , asynchronous communication , discrete time and continuous time , mathematics , linear matrix inequality , jump , matrix (chemical analysis) , population , lyapunov function , markov process , computer science , control (management) , mathematical optimization , nonlinear system , computer network , statistics , physics , materials science , demography , quantum mechanics , artificial intelligence , sociology , agronomy , composite material , biology
Finite‐time asynchronous control problem is discussed for positive Markovian jump systems in this study. The non‐synchronous behaviours generated between the system modes and controller modes are fully considered. To ensure the closed‐loop system positivity and finite‐time boundedness with a guaranteed H ∞ performance level, a sufficient condition on the existence of an asynchronous controller is first established by applying Lyapunov–Krasovskii functional approach and recursive matrix inequality methods. Then, with the aid of matrix conversions, the specific form of controller gain matrices can be constructed by solving linear matrix inequality (LMI) conditions. A numerical example is presented and application is illustrated to validate the proposed results by employing a pest's age‐structured population dynamic model.