Open AccessMixed H 2 / H ∞ control of time‐varying stochastic discrete‐time systems under uniform detectability
Author(s) -
Sheng Li,
Zhang Weihai,
Gao Ming
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.2014.0420
Subject(s) - control theory (sociology) , discrete time and continuous time , mathematics , control (management) , computer science , statistics , artificial intelligence
This study is concerned with the infinite horizon H 2 / H ∞ control of time‐varying stochastic discrete‐time systems with state and disturbance dependent noise. The notion of uniform detectability for time‐varying stochastic discrete‐time systems is introduced, and some good properties are derived. Under uniform detectability, a necessary and sufficient condition for the existence of time‐varying stochastic H 2 / H ∞ control is presented, which transforms the design of H 2 / H ∞ control into the solvability of coupled time‐varying matrix‐valued equations. Finally, an iterative algorithm is proposed to solve the coupled time‐varying matrix‐valued equations, and a numerical example is provided to show the effectiveness of the obtained results.