Premium
Delay‐dependent output feedback L 1 control for positive Markovian jump systems with mode‐dependent time‐varying delays and partly known transition rates
Author(s) -
Qi Wenhai,
Gao Xianwen
Publication year - 2016
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2285
Subject(s) - control theory (sociology) , jump , lyapunov function , controller (irrigation) , transition rate matrix , markov process , mode (computer interface) , mathematics , stability (learning theory) , function (biology) , control (management) , computer science , physics , nonlinear system , statistics , quantum mechanics , artificial intelligence , machine learning , evolutionary biology , agronomy , biology , operating system
Summary The paper deals with the problem of delay‐dependent output feedback L 1 control for positive Markovian jump systems with mode‐dependent time‐varying delays and partly known transition rates. First, by constructing an appropriate co‐positive type Lyapunov function, sufficient conditions for stochastic stability and L 1 ‐gain performance of the open‐loop system are developed. Then, an effective method is proposed to construct the output feedback controller. These sufficient criteria are derived in the form of linear programming. A key point of this paper is to extend the special requirement of completely known transition rates to more general form that covers completely known and completely unknown transition rates as two special cases. Finally, a numerical example is given to illustrate the validity of the main results. Copyright © 2016 John Wiley & Sons, Ltd.