Open AccessFinite‐time analysis and design for discrete‐time switching dynamics Markovian jump linear systems with time‐varying delay
Author(s) -
Wen Jiwei,
Peng Li,
Nguang Sing Kiong
Publication year - 2014
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.2014.0622
Subject(s) - dwell time , control theory (sociology) , upper and lower bounds , discrete time and continuous time , mathematics , markov process , jump , piecewise , controller (irrigation) , interval (graph theory) , linear system , computer science , control (management) , mathematical analysis , physics , medicine , clinical psychology , statistics , quantum mechanics , combinatorics , artificial intelligence , agronomy , biology
The problems of finite‐time analysis and design for a class of discrete‐time switching dynamics Markovian jump linear systems (SD‐MJLSs) with time‐varying delay are investigated in this study. The considered systems could be viewed as Markovian jump linear systems governed by a piecewise‐constant transition probability matrix, which is subject to a high‐level average dwell time (ADT) switching. The time delay is considered as time varying and has a lower and upper bound. First, sufficient conditions, which guarantee the stochastic finite‐time boundedness of the underlying systems, are presented by employing the ADT approach. These conditions are not only dependent on the delay upper bound but also the delay range. Then, a finite‐time weighted l 2 gain of such delay SD‐MJLSs is obtained to measure the disturbance attenuation capability over a fixed time interval and the design of the stabilising controller is further given. Moreover, an improved controller design method, which could provide efficiency and practicability, is further developed. Finally, a numerical example is given to verify the potential of the developed results.