TY - JOUR
T1 - Robust variance-constrained H∞ control for stochastic systems with multiplicative noises
AU - Wang, Zidong
AU - Yang, Fuwen
AU - Ho, Daniel W.C.
AU - Liu, Xiaohui
PY - 2007/4/1
Y1 - 2007/4/1
N2 - 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. © 2006 Elsevier Inc. All rights reserved.
AB - 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. © 2006 Elsevier Inc. All rights reserved.
KW - H∞ performance
KW - Linear matrix inequality
KW - Multiplicative noises
KW - Stability
KW - Stochastic system
KW - Variance constraint
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U2 - 10.1016/j.jmaa.2006.05.067
DO - 10.1016/j.jmaa.2006.05.067
M3 - 21_Publication in refereed journal
VL - 328
SP - 487
EP - 502
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -