Robust variance-constrained H control for stochastic systems with multiplicative noises

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Original languageEnglish
Pages (from-to)487-502
Journal / PublicationJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 1 Apr 2007


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.

Research Area(s)

  • H∞ performance, Linear matrix inequality, Multiplicative noises, Stability, Stochastic system, Variance constraint