@article{38b61a69b0cb43ef81edbfaaad630601, title = "Robust variance-constrained H∞ control for stochastic systems with multiplicative noises", abstract = "In this paper, the robust variance-constrained H∞ control problem is considered for uncertain stochastic systems with multiplicative noises. The norm-bounded parametric uncertainties enter into both the system and output matrices. The purpose of the problem is to design a state feedback controller such that, for all admissible parameter uncertainties, (1) the closed-loop system is exponentially mean-square quadratically stable; (2) the individual steady-state variance satisfies given upper bound constraints; and (3) the prescribed noise attenuation level is guaranteed in an H∞ sense with respect to the additive noise disturbances. A general framework is established to solve the addressed multiobjective problem by using a linear matrix inequality (LMI) approach, where the required stability, the H∞ characterization and variance constraints are all easily enforced. Within such a framework, two additional optimization problems are formulated: one is to optimize the H∞ performance, and the other is to minimize the weighted sum of the system state variances. A numerical example is provided to illustrate the effectiveness of the proposed design algorithm. {\textcopyright} 2006 Elsevier Inc. All rights reserved.", keywords = "H∞ performance, Linear matrix inequality, Multiplicative noises, Stability, Stochastic system, Variance constraint", author = "Zidong Wang and Fuwen Yang and Ho, {Daniel W.C.} and Xiaohui Liu", year = "2007", month = apr, day = "1", doi = "10.1016/j.jmaa.2006.05.067", language = "English", volume = "328", pages = "487--502", journal = "Journal of Mathematical Analysis and Applications", issn = "0022-247X", publisher = "ACADEMIC PRESS INC ELSEVIER SCIENCE", number = "1", }