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.